Sir ps2 is play station 2 and ps3 is platstation 3. Sony launched a normal play station 2 version and then it bring the slim ps2 in 2006 I guess! Slim is like updated version. Games supported are mostly till 2010-2011. It used dvd playback for games.
ps3 is advanced when it was launched in 2008 I guess It was costing 40k in pak a highly advanced console with wireless controllers. It has ability of blue ray player and you can use it for games till date. and it will play movies too!
A pakistani example would be like Ps2 fat is Iphone 3g and slim is 3gs. While ps3 fat is i phone4 and slim is 4gs.
Hope I cleared my point!