The cask project supports large binaries and projects whose licenses are a little more poisonous than your standard brew libs. tap as far as I can tell is basic

The cask project supports large binaries and projects whose licenses are a little more poisonous than your standard brew libs. tap as far as I can tell is basically the same as PPA extensions in linux, it lets you install stuff from external repo lists. PPAs were pretty standard fare when I used to use linux more often, maybe working with package managers in your distro of choice for a while will help. In practice you usually don't need to use either cask or tap 99% of the time.