REAPER and Ardour and ProTools - Multitrack recording tools, used for recording live performances, with some basic MIDI capabilities built up over the years.
Cubase and Logic - MIDI sequencers, with multitrack capabilities accreted over many years to the point where multitrack recording (in the same contexts as the above category) is not unheard of, though the UI focus is different.
Fruity Loops and Ableton Live - Loop composition tools (for lack of a better description). Both are designed around loops as the basic building block of sound. While they have limited recording and MIDI capabilities, one likely wouldn't use FL or Ableton to make a symphonic soundtrack for a film, and certainly wouldn't use either to record a full band of performing musicians.
Renoise and apparently Radium - Trackers for the current century. These evolved out of the old Soundtracker style music programs (including Protracker, MED, etc. on the Amiga and then onto FT and Impulse Tracker on early PCs). They've acquired most of the functionality one expects from sequencers and loop based music programs, but don't usually have any multi-track recording facilities.
All are called DAWs by their developers and users, and yet how one uses them is pretty different. I pretty regularly use Ardour and REAPER for multitrack recording. And, I occasionally use Fruity Loops and LMMS for tinkering with remixes. And, I occasionally use Renoise for making electronic music.
I'd like it if there were separate terms for each of these concepts, as it would give folks a good language for talking about what each of these types of tools do. It would also rule out a lot of the stupid confrontational crap that often comes up ("Your program sucks because I can't do X, Y and Z, and I only ever use this other program!" where X, Y, and Z are functions specific to one of the above types of DAW...like "I can't easily do loop-based remixes in ProTools. ProTools sucks!").
I wouldn't say that one certainly wouldn't use Ableton to record a full band of performing musicians. Because I've tracked multiple bands in Ableton. I patched my rig into SSL G and J-series consoles at mid to large sized studios, rather than using the in-house Pro Tools setup.
I worked as a recording engineer for 7 years before becoming a programmer, and I've seen top engineers doing things that I thought was a horrible idea, but they would end up with amazing sounds.
Otherwise, I agree with the other stuff you're saying, just felt like nitpicking about that.
Yes, there's tons of overlap in all of these (sequencers and multi-track recorders were the first to begin to blur the lines, but now basic loop-based features are creeping into sequencers and both FL and Ableton can be used for nearly any basic sequencing task), but the focus of the tool makes a difference in workflow.
And, the tools that pros use for specific tasks can also be indicative. You won't be surprised to find ProTools in a high end recording studio, and you won't be surprised to find a film soundtrack composer using Logic or Cubase. Likewise, you won't be surprised to find an EDM producer using Ableton. There's less overlap in what pros use than in what the tools are capable of in the hands of someone really good with that specific tool.
Anyway, doesn't matter. My point is that there are several different categories of program called DAW. The way they display and receive data varies wildly, and the use cases for them is pretty diverse, and I think it's weird to call them all the same name.
It's strange to have Ardour and Reaper up there with ProTools and Logic described as a MIDI sequencer. That's how it started but at some point it crossed over into a full-featured professional DAW and I'm not sure even Reaper has caught up to its live instrument mixing and editing capabilities.
Ableton is literally a sequencer (and much more) and probably belongs in your MIDI sequencer category.
No, the point doesn't hold up. That's like saying 'workbench' or 'car' is too general to mean anything. It's a general category and you put adjectives in front of it as needed.
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.
I said not all of these things should be called "DAW", but they are all called DAW by many people. I'm saying that is confusing terminology and I wish we could settle on calling some of these things something else. I don't care which things get called "DAW" and which ones get called crows or other types of corvid.
But, the term "DAW" is overloaded, and one of the negative side effects of that overloading is that whenever the discussion comes up somebody has to argue that a bunch of these things that people call "DAW" are stupid and we should hate them because they aren't good for X, Y, and Z. As you have eloquently demonstrated.
Were you trying to demonstrate that fact?
Also, I not only had no intention of derailing OP's question, I answered it by explaining that Radium is in the "modern tracker" category.
To be clear, I'm not agreeing with you and it's bizarre that you think I am. The term DAW is just fine, it's not overloaded and I found grandparent comment's usage of it to be perfectly clear.
Rereading your post I see you did put Radium under your 'modern tracker' category, I think I was so appalled at how you described the other products that I didn't pay attention to where you put it because at that point you had already demonstrated the depth of your knowledge.
It seems pretty tracker-like, with columns for instruments and rows containing notes, but what makes it different is the focus on graphical editing and automation. The node editor thing on the right for connecting effects looks pretty cool, too.
It looks like it is indeed a DAW (supports VST and LADSPA, which is a tell-tale sign), but with a lot more/better features and a pretty visible tracker heritage.