Please do not call, what we Realtors do, an APPRAISAL:
Only Appraisers do an Appraisal.
Realtors do a CMA, or Comparative Market Analysis.
If both are done correctly, they should be close; I wouldn't guarantee that they will match up.
The two people may use different Comp houses, they may be done at different times, (even a week or two could make a difference), they may see different features and upgrades in all the houses, they may assign different values to features and upgrades:
This is not an exact science and the numbers are dynamic; constantly shifting.
Do not use one set of numbers as a weapon against the other. Not fair!