Can you explain the county tax appraisal on my house?

In Realtor’s school recently they gave an example of a house apprising for tax purposes for far less than it was actually worth on the market.

I asked the instructor what it means when the house appraises, for tax purposes, for more than it’s market value. She said that would never happen. That caused my brain to trip because I KNOW they’ve always taxed it above its market value.

Or….maybe I misunderstood what she was talking about. Today I called the tax office. They said for their purposes the house appraised at $87,690.
However, my house’s market value was recently (in the last two weeks) appraised at $82,000. I paid $75,000 for it in 1998.

What am I missing? Should I look further into this? What should I do next?