Full House - Old Friend? New Friend?
Okay this was pretty obvious to me, so I was unsure why it hadn't been mentioned yet. In one of the episodes where they are showing Michelle on "Ranger Joe", she is introduced to Denise (I want to say it's the episode where Michelle is confused about why her little boy friends do not like her being a girl). Farther down the road, when her best friend Teddy moves away, Michelle gets a new friend in class... and it is also Denise... yet they are acting like they've never met before.