Is someone with a phd in professional counseling vs phd in psychology still considered a psychologist?

Yes but not exactly: A Ph.D in Counseling Psychology would be considered a psychologist. Different states have different regulations around the title of psychologist so check with a state licensing board to be sure. For example, Vermont is now the only state where a person with a Master's Degree in Psychology can be called a Psychologist, provided that they indicate Psychologist-Master.

Yes: Both are considered doctors. Both would be considered psychologists if licensed by the state / area where they practice. Some areas may give different privileges to doctors with clinical psychology versus counseling doctorates, others do not. In CT, where you live, both could be licensed as a psychologist if they have a PhD, passed exams, & completed the other requirements.