County Appraisal vs. Purchase Appraisal

[Quandra Adams]

I just received an appraisal letter from my county for my property. It is almost $20,000 less than the purchase appraisal price. If I do not correct the county and leave the lessor property value price in place and benefit from the low taxes, what are the consequences and repercussions in the future if any? 

I do understand that if I correct them and they increase the value that my taxes go up and result in a higher monthly mortgage bill. 

I also see a space where I can select that this is an income-producing property. What does the county do with that information in terms of assessing value? 

I'm a complete newbie here and this is the first year of me owning this property so any and all information is greatly appreciated.