Does the Market Value of a Home Raise the Appraisal Value?

First time homebuyer here.

My realtor told me that if I buy a house, that has an appraised value of 130k, for 180k, that it will raise the appraised value to 180k. So, that means I will be paying taxes on the sell value(180k) of the home I bought. Is this true for Harris County?

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I looked on HCAD and I really don't understand what the guide to understanding property taxes is saying.