Outside of co-counselling a Counsellor is someone who you see to help you try to resolve issues that you have or improve your life in some way. They they have various levels and types of expertise which they can use to help you. The terms "counsellor" and "psychotherapist" are generally accepted as being interchageable.
In CCI Co-Counselling this is different: the client is in charge and 'runs' the session, decides what to work on and how to do this. In the Session Contract the Client and the Counsellor clarify how the counsellor can fill in their supportive role. They even can be asked to be a silent witness.
The core attitude of the Counsellor is Free Attention: witnessing the client with a warm heart and letting them get on with their session. Leaving the Client in charge of their session can be a challenge for a Counsellor. For more information about this, see the Rescue Triangle.
Pending the Session Contract the counsellor can give verbal and non-verbal suggestions.
There is a different, potentially confusing use of the word 'Counsellor' in Germany.
People can only really be in charge of their session if they are able to 'counsel' themselves. It is exactly for this reason that people trained in the Münster approach have decided in the past to call their Clients 'Counsellor'. and their Counsellor 'Co-Counsellor! See for more background of this, the history of Co-Counselling in Münster.