FAT (FAT16 and FAT32) and NTFS are two methods for storing data on a hard drive. The hard drive has to either be formatted using one or the other, or can be converted from one to the other (usually FAT to NTFS) using a system tool. FAT32 and NTFS are file systems i.e., a set of logical constructs that an operating system can use to track manage files on a disk volume. Storage hardware cannot be used without a file system, but not all file systems are universally supported by all operating systems.
All operating systems support FAT32 because it is a simple file system and has been around for a really long time. NTFS is more robust and effective than FAT since it makes use of advanced data structures to improve reliability, disk space utilization and overall performance.