FAT means File Allocation Table
Fat32 is a type of Fat file system.
Fat file system has 3 types
1) Fat12
2)Fat16
3)Fat32
The number in the names of file systems represents number of bits used in the addressing scheme.
More bits means more addresses, so large drives are accessed and addressed through the file system.
Before Fat32, there was FAT16, it was just called FAT.
You can just use FAT32 for your flashdrive.