Hey Phoenix, great article. Thanks for your comment on my article too.
I think you did a great job of filling in the nuance of these terms.
I've definitely received some feedback along the lines of what you're saying: there's a push to relabel homeless as houseless to avoid the negative connotations. I can see why that would make sense. I can also see why some would see that as sanitizing the issue or distracting from what's important.
I don't really know what words are the best to use. I don't actually think that's what's important here... the main thing people need to understand is that "living rough" by choice is a totally different thing than being thrust into that situation with no reliable way out. And it's a hell for a lot of people, and it needs our attention.
Thanks for writing this <3