Okay, how important do I have to be to have my murder become an assassination? I mean, I know that killing the head of the local shriner’s is probably not assassination, but at what point is it? PTA president? County senator?
Probably depends on who’s doing the reporting.
My dictionary says an assassin is murderer who “carries out a plot to kill a public official or other prominent person.” There is an implication of political motive and plot, of course; even if you’re a Senator, and your spouse beans you fatally with a frying pan, that’s just ordinary murder.
OTOH, you don’t need to be public or prominent for me to carry out a character assassination of you.
I think the “political motive” that C K mentions is probably the big thing. So I’d say that if you were REALLY into PTA politics, and couldn’t accomplish your goals any other way, if you were to kill the PTA president, then yes I’d say it’s assassination.
On the other hand, if one of George W.'s old drinking buddies gets pissed at him for not picking up the bar tab 30 years ago and decides to kill him, is that still assassination? It would certainly be reported as such.
Try telling Manhatten that a small Southern town is a better place to live than New York City.
That almost worked, for me. 
The Sheriff-elect of DeKalb County, Georgia was gunned down in his driveway, allegedly as the result of a conspiracy headed by the former Sheriff whom he had defeated for re-election. This has been pretty widely referred to as an “assassination” by both the local and national news media.
It depends on who’s doing the talking. I once heard a radio DJ refer to John Lennon’s “assassination.”