A cylinder has 2 circular faces.
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Two flat faces (one at either end of the prism), and a curved side.
If these forms are all solid, a sphere has one side and face, a cone two, and a cylinder three. If there are hollow, they have one more face than side.
If the cylinder is cut in half along the side it is still a cylinder. If the cylinder is cut in half along one of the circular faces it is a horizontal cylindrical segment, which would look like a pig trough not hollowed out.
A circle comes to mind as the face of a right cylinder (which has 2 faces). The curved side is not considered a face.
Sides and faces are the same thing. A hexagonal prism has 8 faces and 12 vertices.