symbolic vs numerical

always been a bit confused about how to exactly distinguish between a numercial and a symbolic maths solving type of computer program. to be fair its a very grey world and not easy black/white. most numercial programms(like matlab) will have some symbolic abilities(matlab uses a stripped down maple kernel) so for the casual user
ive spent the past hour or so browsing the net to get myself up to speed on what programm is a numerical and which one is a symbolic. the result is that i found this. very helpful. ill be trying MuPAD then. as i have before but now i know what it actually does,]]