I'd say I am a little of both. We do not unschool, so I guess that means I am somewhat of a teacher. I plan our schedule, gather the supplies, and try to keep each day on track. But sticking to the schedule isn't as important as following the varying needs and interests of my daughters.
Certainly I can give a little here and there to keep our lessons interesting and fresh. We might do lessons outside in nice weather. If dd just isn't in the mood to write her lessons, I let her dictate to me. If it is just "one of those days", we junk the lessons and just read or explore the outdoors.
I would say my dd just sees me as Mom.