There is a real definition, and it isn't kitchens. A two-unit property is one where the local zoning and building records recognize two separate dwelling units at that address. The paperwork that shows it is usually a certificate of occupancy, a permit history, or a zoning verification letter from the city. What zoning allows and what proof a city will issue varies by state and often by town, so you check with that specific building department rather than a general rule.
The assessor record isn't proof either way, but it's a hint that the second unit may never have been permitted. Assessors sometimes lag reality by years.
Where this bites is the appraisal. On a purchase, the appraiser decides how many legal units exist and writes it on the report. If the appraiser calls it a one-unit house with an accessory space, your lender underwrites it as a single family home, and the rent from the second unit usually can't be counted toward your income. Your whole reason for buying it goes away at that point.
The part people miss is insurance. Carriers ask how many units and whether the use is permitted. If a claim happens and the unit was never legal, the settlement conversation gets ugly.
So ask for the permit file before you get attached to the numbers. If the unit is unpermitted, the honest ways forward are a lower price and a plan to legalize it, and whether legalizing is even possible depends entirely on your local ordinance.