Basically, a DAW is a music program that does EVERYTHING. Audio editor, sequencer, plugin host, mixer...
Audacity, for example, is just an audio editor. It has some basic midi tools but those were still being tested last I heard. Anvil Studio is, iirc, just a sequencer. Doesn't do plugins. Just midi writing. Unless I'm wrong about what they can do, they're not DAWs.
Note that having a sample library and/or built-in/bundled effects isn't necessary for it to be a DAW. Those are things you may have to get yourself. Fortunately, the internet is full of free stuff. Some of it is even good.
edit: realizing that the remixing faq/tutorial me and zephyr were writing would be really helpful here. You might find this unfinished version useful, just ignore our comments about what needs to be added/changed and stuff.
Thought I had a v1.3 somewhere. Maybe I'll have time to dig it up and update it this week.
edit2: reading through it, there's a lot I need to change. Most of it is ok, but I'd check with other sources to get stuff like the order of effects right. The part about samplers is a little confusing because sometimes we've misspelled samples as samplers. Should be fixed it later versions, but that's the version I've got online.