Some idioms for "psychotherapist" and the meaning of "therapist" in the US

Yes, it's generally true. Other forms of therapist are normally more beholden to include their type: physical therapist, speech therapist, etc. In fact, the use of "therapist" is far more common than the use of "psychotherapist". Unfortunately for some medical doctors, "therapist" also tends to refer to a psychiatrist despite a difference in education requirements.

"Headshrinker" and the more common "shrink" are (mostly insulting) idioms for a psychiatrist or psychotherapist. "Counselor" is also used for a therapist, particular one who conducts guided therapy in couples or groups.

"Therapist" increasingly refers to a physical therapist - (although it is still more common to assume "head-shrinker" in conversation) to remove the ambiguity, the term "analyst" is also common, and more precise. (US)