How would we know. Your bank is the one using the appraisal so ask their appraiser .

It's possible that one is measuring from exterior wall to exterior wall and the other is measuring inside wall dimensions. There may be some local custom around it - it's my understanding that in my area exterior dimensions are used in real estate listings. Also, any of these dimensions may be approximate depending on how they're done. Did the person doing the dimensions take a half hour doing it, or two hours? Unless the home is a perfect rectangle on both floors getting the correct measurements is going to be somewhat time consuming. Is one measure based on blueprints and the other based on quick measurements?

Appraisers are now required to measure homes using specific guidelines (ANSI) for most transactions. Prior to this we measured according to local custom or practices. If you home has a two story foyer or two story family room the area above may have been included in the gross living area calculation in the first report and then not included in the second. That would explain the difference.

The sq ft difference might be on what you can walk on verses overall size. For instance, a room with a vaulted ceiling: it has a two-story size, but you can only walk on the bottom part; ergo… less footage.

There are two posts on this subject. To the OP it would be advantageous to you to stick to one.