People's answers are correct, but I think sometimes we're so used to using some of the same technical terminology that we forget to explain what they mean sometimes. The question of using conduit or not doesn't depend on the wire thickness; it's more about how/where you are running the wire, and that also relates to the wire types.
What is called NM-B or "Romex" is that multi-wire bundle with the black rubber sheath you have probably seen. That is approved for just running inside of your walls directly, without the need for conduit.
The ones that are referred to as THWN or THHN are individual wires. So you might select to run 2 or 3 or however many separate conductors you need for the outlet or device you're putting on. Those can't just be run loose in your wall where the insulation is, so they would run on the outside surface of a wall, and since they are not attached together, they would all need to be placed in some kind of conduit.
So then when you have picked how you are going to run it, whether cable inside the wall, or separate wires in conduit outside the wall, that kind of picks your wire type. Then you can look up in that ampacity table what thickness of wire you would need for the specific size of circuit you are going to do.
I hope that explains the basics a little better.
