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.