From school here's what I learned...it's not extremely thorough, but it is to the point.
FAT16 is old/obsolete. Users can only have make a 516MB disk space, it's extremely vulnerable, and file names can only be something like 8 characters long.
FAT32 is an updated version of FAT16. Here users can have a max of some where around 1GB of diskspace. It's still pretty vulnerable and users can have longer file names (I think).
NTFS = New Technology File System
This is one of the more modern types of file systems created by Windows. Though buggy and tempermental, it's more secure and whatnot. It can recognize any size hard drive (as long as the motherboard supports it) and can support extremely long file names.
The main difference between them is cluster size they used.Cluster is a set/group of sectors.
It maintain a table(which is called file allacation table) where each entry is of 16 bits ,pointing one cluster.Therfore there is 2^16 entries in a table.Hence tot no.of cluster supported by FAT16 is 2^16(=65536).
If u use "fdisk" dos command to create a partition of FAT16,then each cluster size is 32KB and a sector size is 512 B.
Now , No.of sectors in 1 cluster=cluster size/sector size=32KB/512B
=64 sectors per cluster.