First, note that there are three varieties of FAT: FAT12, FAT16, and
FAT32. Many people call FAT16 just FAT, because before FAT32 came out,
FAT16 was the only variety used for hard drives, so just calling it
FAT was sufficient.
FAT12 (hardly used at all anymore) had a maximum volume size of 12mb.
It was used almost exclusively for floppy disks.
FAT16 was used on hard drives (or partitions) up to 4GB, and had a
cluster size that varied from 2kb to 64kb, depending on the size of
the partition. It is almost never used anymore, because almost nobody
has partitions as small as 4GB.
FAT32 took over from FAT16 and has a maximum drive size of 2TB. Its
maximum file size is 4GB, which is why you can't copy a 5GB file to
it. Its cluster size is 4KB up to a partition of 8GB. Above 8GB the
cluster size grows up to 32kb.
NTFS is what almost everyone should be using on their hard drives
today. Its maximum volume size is 2^^64-1, and its maximum file size
is 16 × 1024^^6 bytes (way more than the biggest hard drive available
today). Its cluster size stays at 4kb, regardless of the volume size.