Here's the difference.
Qing dynasty ruled Tibet.
Qing past the government to republic of China head by then temporary president Sun ZhongShan(Mandarine spelling, the right one.)
Sun, later created the republic of China government again and incorporated the communist party in his three policies.
Communist party was purged by Chang, and so started the civil war.
Communist won and we inherited the country from Sun.
Do you see this link? We inherited from republic of China which inherited from Qing, which includes Tibet.
Pakistan and India agreed from the British on the split, so any claim was forfeited, and any other claims are not direct claims. The dynasties changed, and the succeeding dynasties are not necessarily include all the occupier's territory.
For example, Ming China took China back from the mongols, but we don't have rights to Russia and middle east, because it is not the successor to Mongols, but rather broke apart from Mongols.
People's republic is the direct successor to the republic of China which included Tibet, and Qing dynasty which also included Tibet. We were just too busy with civil wars, weakness and Japanese to take care of Tibet separatists.