I try to make a point of saying "ranger-qualified" when talking about my own service, but most people, both in and out of the service, just don't know any better. So, they will tell their buddies or other people that I'm an Army Ranger. If someone asks if I'm an Army Ranger, I'll say, "Yeah, I'm ranger-qualified," or something similar. I will not bother to explain in great detail the difference unless asked for clarity or it becomes the explicit subject of the conversation, nor do the 99.9% of people care. In fact, I would argue that the only folks I've come across that take issue with any of it are a subset of those who specifically served in Ranger Regiment, and specifically the first 3 battalions of Ranger Regiment.
What I will not do is explicitly state that I served in a Ranger Bn, and that's despite the fact that I served in a special operations unit in Iraq doing an unconventional job normally reserved for a Ranger Bn, who were at the time being over-deployed, and were broken into platoons filling an unusual mission-set even by their standards... So, my conventional battalion filled their role within the task force. Nevertheless, that doesn't make me a Ranger in the same sense as those who served in a Ranger Bn. I think the point made above about the Ranger hall of fame including tabbed-only "Rangers" is an interesting one. I'd also make an interesting-to-me point: there are plenty who served as a real, bona fide Ranger-Battalion-assigned "Rangers" who never got the tab. There were also plenty in support roles within those Battalions who didn't do an infantry mission while assigned or attached. I remember a Supply NCO friend of mine that was assigned to a Bn for a time. They are Rangers and can rightfully call themselves such, as they served as a Ranger within a Ranger unit. Nevertheless, I take nothing away from those who served in Regiment. To the contrary, ALL the props that go their way are deserved. In general, though individual experiences vary, they have a harder life, higher OPTEMPO, more frequent deployments, a riskier mission, and they deserve to be recognized distinctly from Ranger-qualified, but otherwise conventional, Soldiers.
In Tom Cotton's case, I would cut him some slack, because I believe it's the job, or at least the current nature, of political opponents to crucify their opposition wherever possible. If Cotton made an explicit statement that he served in Ranger Regiment or Bn without actually having done so, then he deserves to be called out for lying. Otherwise, let it go... I'm pretty confident he did not misrepresent his service. The perceived misconception among civilians and even most service members is too common to worry about.
The last thing I'll leave you with is that at Ranger school they instill this creed into you to the point you can recite it from rote, and I hold it as much my creed as anyone else's, regardless of unit affiliation: