There often isn't a difference - it could come down to whether the therapist calls themself a counsellor or psychotherapist. It could also be related to their qualifications or professional registration. The key differences are with Psychologists, who study doctoral specialisms(clinical, educational, counselling, etc) and psychiatrists who have medical degrees.
The other thing to think about is the type (modality) of therapy.
CBT and REBT are quite problem-focussed and help us to find ways out of difficult and often cyclical problems. They don't tend to focus on the past.
Psychodynamic will focus on the past, childhood, past trauma, etc.
The best thing to do here is research - remember that many now offer online therapy - depends how much you want to do face to face sessions.
Look for someone whose online profile appeals to you - they will always start with a short (free) chat about what you are hoping to get from the therapy.
Trust your gut feeling - if you like them, it's worth a pop. There has been research that shows that the quality of the therapeutic relationship is more important than the modality.