I wouldn't call a 2000 a professional player.
what separates a 1950 from a 2000 player?
A 2000 is no way a professional, that would only occur (hardly) above 2300.
A good amateur ranges from 2000-2200, a CM from 2200-2300.
"what separates a 1950 from a 2000 player?" Not much really, a slight peak of form, a slight peak of motivation or luck, etc.
There are no considerable differences between players separated by less than 100 points, at this level of play.
what separates a 1950 from a 2000 player?
A psychological barrier usually as there is no huge difference in ability - if you are rated 1950, simply set your goal as 2100 and you will pass 2000 without noticing
agree 100000%, try for judge and if you dont make it, hey at least you'll be lawyer, same thing with docs and nurses. same thing with chess ratings. aim for 2100 and if you dont make it , hey at least youll make it to 2000
In my view it is Chess Tactics - thats what took me over 2000 FIDE. Lots and lots of chess tactics study. That and brushing up my endgame - it is amazing how many "really good" players can still make endgame mistakes.
Take a look at "Endgame Preparation" by Jon Speelman and its companion book "Analysing the Endgame" - they are small books but worth their weight in gold! 
No lame jokes like (50pts duhh) but really I know similar things have been asked in the past but I feel this difference is most critical cause it separates the world of amateurs to pros in a way so I wanted to know the difference if any?