The Unix directory structure, unlike Microsoft Windows, has a single top directory (customarily known as the root directory) instead of one top directory per drive. The root directory and its children take up one partition, but you can attach other partitions at arbitrary places inside this directory tree to invisibly attach them.
Linux partitions are where Mastodon lives. These partitions are actually the Linux ext2 filesystem (the de facto standard Linux filesystem) and Mastodon knows how to mount and format them. When you attach a Linux filesystem to your mastodon installation, you will be asked if you wish to format it (unless it is the root (/) filesystem, in which case it will be formatted automatically.)
DOS partitions are used by various Microsoft operating systems. Mastodon can see these partitions, and you may attach them to your mastodon installation anywhere except as the root filesystem, as the /boot filesystem, and a few other places (If you try to attach as DOS filesystem in a forbidden place, Mastodon will complain and refuse to let you do it.)