vfat & FAT32
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.