BACP registration means that you've either completed an accredited training course, which includes a minimum number of supervised counselling hours or that you've completed a training course and completed a certificate of competency set by the BACP. After registration you commit to continued regular, monthly, supervision and continued training and development and that you work within their code of ethics.

BACP accreditation means that you've been fully qualified for at least 1 year, have done over 450 hours of supervised practice and have completed tasks which speak to your ability to understand therapeutic process at a complex level and have a commitment to your own personal development/growth. Accredited counsellors still have a minimum regular supervision requirement and need to take part in regular continued professional development. BACP audit both registered and accredited members to ensure they meet supervision and professional development requirements.

It's not a guarantee of competence but it does mean the therapist has been committed to the process of evidencing their practice. There's a better chance I think of finding someone competent and ethical if they are prepared to work towards and pay for what is a fairly onerous and expensive process of accreditation.