Yes.  Living space. 

"Square footage, acreage, and other information herein may have been received from a variety of sources and has not been verified. If important to buyers, buyers should conduct their own investigation." Listing agents tend to include some verbiage like this under agent comments. 

heated and cooled finished space.

Yes... and the rules for measuring square footage in North Carolina are very specific. Since we still have no code requirement for air conditioning, we measure only heated living area... and then there are all sorts of other rules about how to calculate square footage in specific areas. And we measure to ANSI standards.

One of the first things they teach in real estate school here is to never, ever to use tax records... they are notoriously inaccurate. And our MLS requires that any reported square footage cannot be more than 6% off.

The short story is living space above ground

Long has this been a subject of dispute, inaccuracy and debate. Definition lies in the person doing the professional assessment, but the buyer, seller, and investor have the final say as to whether to accept, reject or modify. 

Generally livable space, sometimes livable space above ground, it really seems to vary be locality.  We just put down what the assessor says.

The total number of one foot square LIVEABLE floor space. Best use a laser measuring tape. Standards VARY state by state there is no National rule. ANSI calls it "Measurements taken and reported on the sketch or floor plan to the nearest inch or tenth of a foot, and the final square footage calculations are reported to the nearest whole square foot."

Some local variation and interpretation but generally living space that is heated and cooled. That said sometimes finished basements are excluded.

We use SF under heat/air and SF total under roof which includes garage space, overhangs, etc.

What Kathleen Daniels, Probate & Trust Specialist said; spot on.

Here I've always gone to the City Assessor's website where it breaks it down. What ever they say is what I listed it as.

Living space.

Not a garage.

Yet...how is a stairway "living" space? If you have a two story house and a one story house with the same square footage stated, are they really the same size?

Heated and cooled living space - no garage etc.

Our MLS has several choices for the source of measurements. Property Records, Measured, Appraisal and Other. ( construction plans)

Usually the heated and cooled square footage is used and there is another MLS  entry line for other sqft which is the garage, porches and decks as shown in the Property Appraiser website. 

Th information is deemed accurate but verification by Buyer or Agent is still recommended if there are any doubts about accuracy. 

Liveable space.

We have total space and living space

Yes, but I never want to try and verify published data.  Impossible to duplicate.

Yes, I do.

Liveable space above ground - not garage. It can vary depending on who is doing the measuring.

Livable space, and with an addition, is it wired and/or heated and Air Conditioned?  I'd also like to add that buying a house using square footage as a factor (perhaps the only one) is an awful way to buy a house.  First, that doesn't include the land underneath.  It also doesn't include the view.  Does it overlook an ocean or a junkyard.  Where is the square footage?  Is it in wide hallways, or closets.  How about the number of bedrooms and bathrooms. Good schools or bad schools.

I think this is why iBuyers are really making some poor decisions, because they factor only square footage by some price factor.

Heated living space.

Yes, What Nina Hollander, Broker said. It's finished and heated space over 5'. Air conditioned not required although it should be in my opinion.

Exterior measure, 7 foot ceiling height. 
You replied with a good list.

About 70% of homes here are co-op's, In co-op's you are buying shares in a corporation, not real property. A buyer is not buying sq ft- so sq ft numbers are often not provided. When it is provided- it's a rough estimate. For condos - it is fair game to use any number found in the offering plan. The challenge here is that the number can be usable sq ft, gross sq ft, or even (and I don't think this is reasonable) gross sq ft plus common area allocated to the apartment.  Most agents use the gross sq ft as this is the most common measurement used. 

In our MLS it is broken up into above ground living space and finished basement living space. In our area basements are quite common. 

All of the living space within the house.

There is livable sqft that usually in public records and actual sqft that includes large roof patios, covered balconies, covered attached garage, etc. I just had 2 surveys on the same property( attached townhome)  and it came with these two numbers. Public record=1900 sqft , survey: 2600 sqft living space+400qft garage and patio. I highly recommend to order the size survey inspections especially on  Single Family Residences.