And if you're going to eschew the term and use descriptions instead, then it's important to get the descriptions right and not arrange them just so your favorites are up top next to ProTools even though they don't belong there.
Better categories: Professional DAWs - these do everything well: ProTools, Logic, (maybe) Cubase. Consumer DAWs - these aim to do most things well: Reaper, Ardour, GarageBand. Sequencers - geared for hip-hop and electronic music: Ableton Live (yes, it's awesome and will probably become full-featured), Fruity Loops. Trackers....
My point is being fussy about the term DAW derailed GP's question, when they asked if it's a DAW they're asking if it's a general purpose or specialty platform which is frankly a good question.