Counseling / Psychotherapy
Though not listed as synonyms, the definition for both terms include providing professional help for emotional problems.
What you are seeking is help for a situation from a professional.
As the consumer you may use either term.
Sometimes one area of the country is more familiar with one term than the other.
Licenses will differ; education will differ.
The title may matter in terms of comfort for you. This is fine.
When you get into the room with this person, the exactness of the definition will fade.
Is there a rapport? Can this provider understand the situation? Will you get what you need?