But murder and manslaughter aren't simply "kill a person with intention", "kill a person without intention", that's why we have different degrees of each. Because you have to define what intention means. Savagely beating somebody to death, while believing they'll probably survive - is that with intention or without? There's also other forms of homicide than just manslaughter and murder!
I think that's why these terms exist, because they become shorthand for longwinded definitions that may need to be very precise.
FWIW, judges in England (or maybe UK) have flip-flopped on this question as recently as in 2003. (See "R v G") That said maybe the problem is that the UK doesn't have different degrees of murder. But still.
Real life can be complicated and moral/legal questions can be hard to determine.
I think that's why these terms exist, because they become shorthand for longwinded definitions that may need to be very precise.