Counselor is a noun. It refers to a person who gives advice (counsel). It is often used to refer to a therapist, a psychoanalyst or a shrink.
Councilor refers to an individual who is a member of a council (official organization).
1. Mrs. Saxena was greatly disturbed about her son's wayward ways and decided to visit her counselor.
2. During the school assembly, the Principal informed the students that they could approach the school counselor at any time if they had any problem.
1. The townsfolk were very happy when their Councilor agreed to release funds for the improvement of the roads.
2. The local Councilor warned residents of the impeding storm and to stay indoors.