If you want a swamp to give cover like woods, you'll need to make it a woods hex. Swamp is terrain modification. If you put swamp on a woods hex, it provides cover; if you put swamp on a clear hex, it doesn't. If a hex doesn't say anything but "Swamp", then it's a clear hex with swamp.
A BT swamp can be either a geological swamp or a marsh, depending on what it is paired with (woods or clear).