I am only familiar with the laws of OR, WA, MA, CA, and CO – the states where I'm considering doctoral programs – but "therapist" and "counsellor" are regulated and require one have a license to advertise with them. "Life coach" is the only title I am aware of that is completely unregulated across the US.

Psychoanalytical Therapist is perhaps the caveat you're thinking of? I know in New York it is a regulated title, and it may be possible to practice independently without a Counselling or Social Work degree provided one isn't billing insurance or advertising as a "psychotherapist".

Here is NY's list of licensed professions: http://www.op.nysed.gov/prof/

Psychoanalyst is a regulated title, as are certain mental health professional titles which include the words therapist or counselor as part of the title.

But neither therapist or counselor standing alone nor psychotherapist is regulated there. (Nor is psychoanalytical therapist, unless something like case law has found that to be too confusingly similar to psychoanalyst.)

I'm not disputing your examples from other states. Just saying that these titles are significantly ambiguous across North America because of their inconsistent status, and therefore there's no standard of treatment which one can assume for them without knowing the precise state or province in question.

In my home state Therapist is a regulated term, as is Counselor. There are two different licenses, LMHC and MFT with LMHC being a good indicator that you're not going to a quack. MFT does have some educational requirements but they're satisfied by religious vocational training. It was a helpful filter for me.