What is the difference between VFAT and FAT32 file systems?
FAT32 along with FAT16 and FAT12 are file system types, but vfat along with umsdos and msdos are drivers, used to mount the FAT file systems in Linux. The choosing of the driver determines how some of the features are applied to the file system. For example, systems mounted with msdos driver don't have long filenames (they use the 8.3 format). vfat is the most common driver for mounting FAT32 file systems nowadays.
History:
FAT, initially was a filesystem that did not handle long filenames. For W95, Microsoft (and other companies) introduced a new method to handle long filenames. That was the same FAT filesystem (FAT16 usually at the time) but with this new method on top of it called VFAT. Microsoft created the virtual device driver, embedded in W95 that was able to have a FAT16 filesystem with long file names feature. That feature is the VFAT. In the Linux world, up to that point, it was common to use the driver "msdos" to mount FAT12/16 file systems. Then, in order to handle this new feature on top of FAT filesystems, it was created the vfat driver (the driver umsdos that came before also handled long filenames), which could mount FAT16 drives in Linux with long filenames. Every time you see that your file system is VFAT, it means it is a FAT file system with the ability to deal with long filenames.
Source: this Wikipedia article
Output of commands like df and lsblk indeed shows vfat as the file system type. But sudo file -s /dev/<partition> shows FAT (32 bit) if a file system is FAT32.
You can confirm vfat is a module and not a file system type by running modinfo vfat.
Copied from http://technet.microsoft.com/en-us/library/cc750354.aspx
What's FAT?
FAT may sound like a strange name for a file system, but it's actually an acronym for File Allocation Table. Introduced in 1981, FAT is ancient in computer terms. Because of its age, most operating systems, including Microsoft Windows NT®, Windows 98, the Macintosh OS, and some versions of UNIX, offer support for FAT.
The FAT file system limits filenames to the 8.3 naming convention, meaning that a filename can have no more than eight characters before the period and no more than three after. Filenames in a FAT file system must also begin with a letter or number, and they can't contain spaces. Filenames aren't case sensitive.
What About VFAT?
Perhaps you've also heard of a file system called VFAT. VFAT is an extension of the FAT file system and was introduced with Windows 95. VFAT maintains backward compatibility with FAT but relaxes the rules. For example, VFAT filenames can contain up to 255 characters, spaces, and multiple periods. Although VFAT preserves the case of filenames, it's not considered case sensitive.
When you create a long filename (longer than 8.3) with VFAT, the file system actually creates two different filenames. One is the actual long filename. This name is visible to Windows 95, Windows 98, and Windows NT (4.0 and later). The second filename is called an MS-DOS® alias. An MS-DOS alias is an abbreviated form of the long filename. The file system creates the MS-DOS alias by taking the first six characters of the long filename (not counting spaces), followed by the tilde [~] and a numeric trailer. For example, the filename Brien's Document.txt would have an alias of BRIEN'~1.txt.
An interesting side effect results from the way VFAT stores its long filenames. When you create a long filename with VFAT, it uses one directory entry for the MS-DOS alias and another entry for every 13 characters of the long filename. In theory, a single long filename could occupy up to 21 directory entries. The root directory has a limit of 512 files, but if you were to use the maximum length long filenames in the root directory, you could cut this limit to a mere 24 files. Therefore, you should use long filenames very sparingly in the root directory. Other directories aren't affected by this limit.
You may be wondering why we're discussing VFAT. The reason is it's becoming more common than FAT, but aside from the differences I mentioned above, VFAT has the same limitations. When you tell Windows NT to format a partition as FAT, it actually formats the partition as VFAT. The only time you'll have a true FAT partition under Windows NT 4.0 is when you use another operating system, such as MS-DOS, to format the partition.
FAT32
FAT32 is actually an extension of FAT and VFAT, first introduced with Windows 95 OEM Service Release 2 (OSR2). FAT32 greatly enhances the VFAT file system but it does have its drawbacks.
The greatest advantage to FAT32 is that it dramatically increases the amount of free hard disk space. To illustrate this point, consider that a FAT partition (also known as a FAT16 partition) allows only a certain number of clusters per partition. Therefore, as your partition size increases, the cluster size must also increase. For example, a 512-MB FAT partition has a cluster size of 8K, while a 2-GB partition has a cluster size of 32K.
This may not sound like a big deal until you consider that the FAT file system only works in single cluster increments. For example, on a 2-GB partition, a 1-byte file will occupy the entire cluster, thereby consuming 32K, or roughly 32,000 times the amount of space that the file should consume. This rule applies to every file on your hard disk, so you can see how much space can be wasted.
Converting a partition to FAT32 reduces the cluster size (and overcomes the 2-GB partition size limit). For partitions 8 GB and smaller, the cluster size is reduced to a mere 4K. As you can imagine, it's not uncommon to gain back hundreds of megabytes by converting a partition to FAT32, especially if the partition contains a lot of small files.
Note: This section of the quote/ article (1999) is out of date. Updated info quote below.
As I mentioned, FAT32 does have limitations. Unfortunately, it isn't compatible with any operating system other than Windows 98 and the OSR2 version of Windows 95. However, Windows 2000 will be able to read FAT32 partitions.
The other disadvantage is that your disk utilities and antivirus software must be FAT32-aware. Otherwise, they could interpret the new file structure as an error and try to correct it, thus destroying data in the process.
Finally, I should mention that converting to FAT32 is a one-way process. Once you've converted to FAT32, you can't convert the partition back to FAT16. Therefore, before converting to FAT32, you need to consider whether the computer will ever be used in a dual-boot environment. I should also point out that although other operating systems such as Windows NT can't directly read a FAT32 partition, they can read it across the network. Therefore, it's no problem to share information stored on a FAT32 partition with other computers on a network that run older operating systems.
Updated mentioned in comment by Doktor-J (assimilated to update out of date answer in case comment is ever lost):
I'd just like to point out that most modern operating systems (WinXP/Vista/7/8, MacOS X, most if not all Linux variants) can read FAT32, contrary to what the second-to-last paragraph suggests.
The original article was written in 1999, and being posted on a Microsoft website, probably wasn't concerned with non-Microsoft operating systems anyways.
The operating systems "excluded" by that paragraph are probably the original Windows 95, Windows NT 4.0, Windows 3.1, DOS, etc.