Are you looking for the practical differences from a user's POV, or the internal technical differences, or both?

These Wikipedia entries should get you started:

Postscript Type 1

TrueType

Also, this infographic by Ralf Herrmann breaks down some of the differences very clearly.

the internal technical differences

the internal technical differences

Internally, there are hardly bytes that are the same. The file format is different, the character map system is different, the looking up of glyphs is different, and the encoding of individual glyphs itself is vastly different.

You need to know anything concrete? Locate Apple's The TrueType Font File (a Microsoft Word document! How quaint!) and Adobe's Type 1 Format. Read them both, and you'll see how very little they actually have in common.

In terms of designing glyph outlines, to me the only essential difference is that PS uses cubic béziers while TT uses quadratic.

hhp

only the technology difference.