Outsider do not understand the definition of Malay. This article from Malaysia Kini can give some light on who are the Malays, and different definition between Indonesia and Malaysia.
Anyone who is a Muslim and practice the way of life as Malay, are termed Malay in Malaysia. Thus if a Chinese, Indian, Cambodian, Thai or Vietnamese who is a Muslim, and practise the way of Malay life, are all termed Malay in Malaysia.
The original people of Malaysia are Orang Asli in West Malaysia, and Dusun-Dayak in East Malaysia. The Malays came later around 7th century (as some said), flourished from 14th century Malacca empire (built by a prince from Singapore, descended from Palembang, Indonesia), to present day immigration from Indonesia, most of them are ethnic Bugis, Achenese, Minangkabau, Sea gypsies/ Orang Laut and other ethnic groups from South East Asia, including the Chams from Cambodia and Vietnam. In Indonesian definition, they are not ethnic Malay but for political reason, they are defined as Malay by Malaysian constitution.
And the aboriginal people are called Orang Asli, they are not called Malay.
Extract of prelude and origin of Malacca Empire history.
"In an effort to revive the fortune of Malayu in Sumatra (Indonesia), in the 1370s, a Malay ruler of Palembang (Indonesia) sent an envoy to the court of the first emperor of the newly established Ming dynasty. He invited China to resume the tributary system, just like Srivijaya did several centuries earlier. Learning this diplomatic maneuver, immediately King Hayam Wuruk of Majapahit sent an envoy to Nanking, convinced the emperor that Malayu was their vassal, and was not an independent country.[10] Subsequently, in 1377—a few years after the death of Gajah Mada, Majapahit sent a punitive naval attack against a rebellion in Palembang,[11]:19 which caused the complete destruction of Srivijaya and caused the diaspora of the Srivijayan princes and nobles. Rebellions against the Javanese rule ensued and attempts were made by the fleeing Malay princes to revive the empire, which left the area of southern Sumatra in chaos and desolation.
By the second half of 14th century, Kingdom of Singapura grew wealthy. However, its success alarmed two regional powers at that time, Ayuthaya from the north and Majapahit from the south. As a result, the kingdom's fortified capital was attacked by at least two major foreign invasions before it was finally sacked by Majapahit in 1398.[12][13][14] The fifth and last king, Parameswara (founder of Malacca Empire) fled to the west coast of the Malay Peninsula.
Parameswara (also known as "Iskandar Shah" in some accounts) fled north to Muar, Ujong Tanah and Biawak Busuk before reaching a fishing village at the mouth of Bertam river (modern-day Malacca River). The village belonged to the sea-sakai or orang laut which were left alone by Majapahit forces that not only sacked Singapura but also Langkasuka and Pasai. As a result, the village became a safe haven and in the 1370s it began to receive a growing number of refugees running away from Mahapahit's attacks. By the time Parameswara reached Malacca in the early 1400s, the place already had a cosmopolitan feel with Buddhists from the north, Hindus from Palembang and Muslims from Pasai."
Article of Interest from Malaysia Kini.
Definition of 'Malay' root cause of Indonesian anger
Tourism Malaysia must be congratulated for adopting a brilliant tagline for its international advertising campaigns. In just two words, ‘Truly Asia’, it sums up the essence of Malaysia in a memorable manner. Together with its descriptor - ‘The wonders of Asia in one exciting destination’ – it makes a competitive and compelling case for the country.
Why go to say, Thailand or Vietnam, with their monocultures, when you can have a multicultural experience in Malaysia? Malaysia has no problems with China and India because its claims are explicit; there are people of Chinese and Indian descent who practice some form of their original cultures in Malaysia.
Tourists are not disappointed, as the country is abundantly blessed with tourist attractions – architecture, festivals, food – which are genuinely of Chinese or Indian origin.
However, several Tourism Malaysia advertisements and events have been met with anger in Indonesia.
The root of this dispute stems from the very different definitions of ‘Malay’ in Malaysia and Indonesia. Put simply, ‘Malay’ is regarded as a
‘suku’ (ethnic group) in Indonesia and a
‘bangsa’ (race) in Malaysia and this difference has profound consequences.
Indonesians are proud of their country because of their long, difficult and bloody fight for nationhood and independence. They trace their struggle to 1928, when a congress of young Indonesian nationalists from many ethnic groups and islands proclaimed the ‘Sumpah Pemuda’ (Youth Pledge), which formalised the concept of ‘one country - Indonesia, one people, Indonesian - and one language of unity, Indonesian’.
Significantly, Malay was chosen as the Indonesian national language instead of Javanese, the language spoken by the numerically, politically and economically dominant group in Indonesia. This because Malay was the lingua franca in the archipelago and, therefore, an ethnically neutral unifying force in the new nation.
Thus the Republic of Indonesia began as a social contract between many ethnic groups of various religions, who shared the common burden of Dutch colonialism and who had decided to unite as one nation.
Today, Indonesians regard their nation as made up of more than 300 ethnic groups, with the
Javanese (41% or more than 90 million) being the largest, followed by Sundanese (36 million),
Malay (8 million), Madurese (8 million), Batak (7 million) and so forth. Importantly, the Indonesian constitution guarantees its citizens freedom of choice of religion and ethnicity does not determine religious belief.
Indonesian children are taught this history and national identity from elementary school. They learn about the different ethnic groups that make up Indonesia, with their specific customs, songs, dances, dress and so forth. They are taught that the Lilin dance is Malay, the ‘angklung’ in Sundanese, the ‘Reog Ponorogo’ dance is Javanese and ‘Rasa Sayange’ is Ambonese.
In Malaysia the definition of ‘Malay’ is a political construct which is spelled out categorically in the constitution. A Malay is ‘a person who professes the religion of Islam, habitually speaks the Malay language (and) conforms to Malay custom’.
Given the vagueness of the definition, it is easy to see why Malaysians tend to think that almost anything Indonesian is automatically ‘Malay’. All Indonesians speak Malay/Indonesian, the vast majority of them are Muslim, and therefore, ‘Indonesian’ equals ‘Malay’, with the exception of some items which are explicitly not Muslim, like the Balinese ‘pendet’ dance.
The incident which provoked the most serious Indonesian response was in 2007, when Tourism Malaysia used Rasa Sayang(e) in its ‘Visit Malaysia Year’ advertising campaign. The Malaysian tourism minister’s response to the Indonesian protests was that Malaysia had a right to use this song as it is from a shared heritage in the Malay archipelago.
This was perceived by Indonesians as ignorant and arrogant. (In the Malaysian context, it would be like the Dayaks saying that ‘boria’ is Dayak as it is part of the shared Malaysian culture.)
The Malaysian answer was bewildering to Indonesians because the Ambonese are dark-skinned, with curly hair from their mixed Melanesian, Malay and African lineage - they look like the Orang Asli of Peninsular Malaysia - and are predominantly Christian.
In other words, they do not fulfil any of the criteria that define ‘Malay’. They look different, use a language which is unintelligible to standard Malay speakers and have a different culture and religion from the Malays.
It was unfortunate that the minister Tengku Adnan Mansor took what Indonesians perceived to be a confrontational stance in this disagreement. The situation could easily have been diffused at this stage by him saying something like:
‘All Malaysians love this song and we have been singing it for generations. Since it is a folk song we cannot pay royalties as no one holds the copyright, but we Malaysians would like to thank the Ambonese for sharing it with us by providing five scholarships to their students to study in Malaysian universities.’
It would have soothed Indonesian discontent and promoted Malaysian education in one fell swoop. Instead, Indonesians began thinking of Malaysians as stealing parts of obviously non- Malay Indonesian culture and calling it ‘Malay’, just to attract a few more international tourists.
With the heightened sensitivity since then, any little incident is now played up for maximum political mileage. These disputes are set to occur again and again as the crux lies in the definitions of ‘Malay’.
Given that the conflicting views are closely entwined with the politics and history of the two countries, these definitions are set in stone.
After all, if Malaysians look at themselves from an Indonesian perspective, they would be forced to conclude that there is no majority race in Malaysia.
It is a country where the Malays are the largest minority group, followed by the Chinese, Indians, Javanese, Bugis, Acehnese, Madurese and the indigenous peoples of Sabah, Sarawak and Peninsular
Malaysia, a nation where the majority are pendatang, led by a Bugis pendatang from South Sulawesi. The current Malaysian government will never allow this view to prevail. 
