I'm a real estate appraiser, though I don't do houses, just commercial property. However, I know how to measure a house if I needed to.
Homes are measured based on the outside dimensions, not including spaces like the garage, porch, etc. An appraiser should take exterior measurements then double check with interior measurements. A simple rectangular house measuring 40'x50' would be 2,000 square feet. Your interior dimensions will be smaller of course due to the walls being anywhere from a few inches to about a foot thick. Adding up all the room dimensions is meaningless as it won't include interior walls, closets, hallways, etc. Plus, those numbers are all rounded and may not be entirely accurate to begin with. Also, staircases only count for one floor so you have to deduct that stairwell opening and any other vertical openings on the second floor. There's an ANSI standard for measuring homes that goes into details about when attic or basement space counts as gross living area or if something like a sunroom should count. Basically it boils down to is that additional space the same quality as the rest of the house?
My brother-in-law purchased a house in 2007 that was basically a rectangle and was listed as being 1,600 SF I believe. They thought it felt smaller but made an offer based on comparable sales of similar size houses in the area. Fast forward 5-6 years when he goes to refinance it to get PMI removed. The new appraiser measures it and it's only about 1,300 SF. Looking at the original appraisal obviously the first guy totally messed up or just changed his numbers to fit what was in the MLS because he was 5-10' off on the length of one of the walls. So, they basically overpaid about $25,000 and when they finally sold it a few months ago had basically no equity between overpaying near the top of the market and it being smaller than was represented. The statute of limitations had already passed or they planed to sue the previous realtor and/or appraiser.
Assessor records vary from excellent to crap. Certainly don't trust the MLS or the realtors involved (or the homeowner). Get on Google Maps and use the measurement tool. That should let you know if it's close, though with a two-story house and a garage it can be a bit harder. Don't be afraid to get out a tape measure before you make an offer or actually close on the property. Or you can hire an appraiser to go measure a house and make a nice sketch for probably $100 or less. Some realtors will do this so they have some CYA when listing the square footage. Most will just pull a number from the assessor which may or may not be accurate and then disclaim any mistakes away.