My $.02
An APAR is (as stated before) an Authorized Problem Analysis Report - IBM acknowledges that there is some sort of defect in a software program. This report sums up the problem and instructs the software lab to fix it. (IXnnnnn or IYnnnnn number - and not before long I guess IZnnnnn)
A PTF is (again as before) a Program Temporary Fix and provides a solution for a problem. (Unnnnnn number for AIX) I guess the U is for UNIX).
When looking for a fix on the IBM site you can look for an APAR number or the corresponding PTF number, either way, you'll find one or more filesets at one or more version numbers to download and install to fix a defect (and - hopefully not - introduce many more ;-) ).
HTH,
p5wizard