As Brendan says. The specification in fact tries hard to convince the reader to get that the exact type of FAT really depends not on signatures or will of volume creators but on the partition capacity. Try to read the specification and you will find about this in a very detailed way. Yes it depends on number of clusters:
Quote:
FAT Type Determination
There is considerable confusion over exactly how this works, which leads to many “off by 1”, “off by 2”, “off by 10”, and “massively off” errors. It is really quite simple how this works. The FAT type—one of FAT12, FAT16, or FAT32—is determined by the count of clusters on the volume and nothing else.
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This is the one and only way that FAT type is determined. There is no such thing as a FAT12 volume that has more than 4084 clusters. There is no such thing as a FAT16 volume that has less than 4085 clusters or more than 65,524 clusters. There is no such thing as a FAT32 volume that has less than 65,525 clusters. If you try to make a FAT volume that violates this rule, Microsoft operating systems will not handle them correctly because they will think the volume has a different type of FAT than what you think it does.
page 14 of the fatgen103 document.