TS, if you don't mind, I felt this could be an interesting topic and sometimes we get so accustomed, to racially derogatory terms that after some time they just become acceptable.
My take? You call them terrorists, maybe a better word will need to be invented, but these two terms misrepresent things and will club in even the good guys. What do you call a member of the KKK? A white supremacist, not a Whitist. What do you call a member of the Vishva Hindu Prasad? A Hindu Fundamentalist, not a Hinduist.
1) Muslims need to disown terrorists conducting terrorism in their name. The majority of us do disown them as non-Muslims. The remaining who do consider them muslims, feel fit to condemn them from an Islamic point of view.
Either way is not wrong, as the condemnation gets through. However I feel, non-Muslims would eventually start clubbing all of us together, and we'll all eventually become the bad guys. Next thing you know, Tableeghi Muslims (equivalent of missionaries) would be clubbed as Islamists, since they are going house to house talking up Islam.
Jihadi, too, grossly misrepresents the literal meaning of the word. Jihad is any struggle against something wrong. Conducting neighborhood watch can be considered Jihad. Writing emails to your congressman, and reporting a problem of graffiti in the neighborhood too can be Jihad. Its a very broad term.
Of course your concern is with the ones that will blow you and me up justifying that this serves Islam. Again why define them as anything more than terrorists and mix them up with an originally noble label?
Also would you condemn a Jihadi armed fighter, fighting in some jungle of Africa to protect his village from ethnic cleansing?
So basically what I'm saying is, these things are situational. Removing the situations can grossly misrepresent things and become a trouble for us, who are otherwise neither, but are Muslims, pray five times a day and in all appearances, Muslim. What happens when we're looked at suspiciously? My brother was attacked by drunkards chasing him with a crowbar, shouting "Go back to Saudi Arabia". People in America can hardly talk coherently about Islam, so you can understand the cautionary alarm bells when we say "Islamists, and Jihadists" will cause confusion.