What is the Full Form of NTFS and FAT ?

NTFS - New Technology File System

FAT - File Allocation Table

NTFS
"New Technology File System" is the Microsoft proprietary file system started with the Windows NT family. It is an improved version of the FAT file system and nowadays preferred in most of the modern operating systems, including: Windows XP, Vista, Windows 7, 8 and 10.

NTFS file system has many technical benefits over FAT and HPFS (High Performance File System). Some major improvements include: better security due to the addition of encryption and permission features to restrict access to the users, a capability to recover from some disk related errors which FAT cannot, better disk space utilization and improved support for larger hard drives.

For larger application, NTFS allows files to spread over multiple physical drives.

FAT
"File Allocation Table" is the simplest file system designed for smaller disks and simple folder structures. The FAT file system uses the 'file allocation table' that keeps track of all the files and folders copied to the drive. Two copies of this table are kept on the drive, in case one becomes damaged.

The FAT file system was evolved into 4 versions namely: FAT8, FAT12, FAT16 and FAT32.

How to check whether the drive is formatted with NTFS or FAT
The most simplest way to check the file system of a drive is by going to its "Properties". Alternately, you may check the drive's status in "Disk Management" to identify the file system of all the drives at once.

How To See If a Drive is Formatted as NTFS
One way to check if a hard drive has been formatted with NTFS, or if it's using a different file system, is by checking the drive's status in Disk Management. This is certainly the easiest place to look if you're interested in checking the file system status of more than one drive.