Let me see if I can get close to what you are looking for without too much of the BS.
Basically FAT32 is the old way to storing files (File Allocation Table). It kept the name of the file and it's associated block address location in a table on the hard drive or media volume. When the system requested a read to a file, it would look up the location in the FAT table and then read back the file. But it was an out growth of an older FAT system called FAT16 (the 16 and 32 are for 16bit and 32bit address structures). What's important is that there isn't a whole lot of information held in FAT. the only security descriptors are read, write, archive, time, date etc...no user information. It was also built for compatibility with older 16bit address schemes, so there was a lot of legacy stuff that it had to keep doing.
NTFS (New Technology File System) was a more elaborate filing system that held more informatio and was much more extensible. I'm not sure of the numbers but I think a FAT32 partition can go up to 2GB and that's it. NFTS is really big, really really big...bigger than you will ever, ever build. It also includes security descriptors and permission settings like userID, domain authentication keys etc. It was also built to be somewhat more efficient in it's use of block space, so theoretically it would format more usable space out of a volume than FAT32.
People will correct the errors above, but for the most part NTFS is bigger, does more and is more efficient than FAT32.
As mentioned earlier, FAT32 should be used for compatibility only. I would format external drives with it and that's only if i'm planning to share them with a unix host. I personally still don't trust Unix for NTFS r/w yet. that's my issue.
I would say use FAT for thumb drives and for stuff that you will move to other odd hosts like windows 98 or unix. and use NTFS for everything else.