From one textbook we use in our High School -
A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases of the trapezoid.
And from Wikipedia -
In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezium (/trəˈpiːziəm/) in English outside North America, but as a trapezoid (/ˈtræpəzɔɪd/) in American and Canadian English.
One other textbook in my school follows the Wikipedia definition.
The former definition excludes parallelograms and rectangles. The latter, defines both to be a subset of trapezoids.
How do we address this with students? I'm starting to get objections to the textbook image I posted, with the student either recalling having learned it differently in a prior class, or searching and declaring another source as the contradiction to our textbook. I can offer a response of "This is one of those math naming properties that doesn't have 100% agreement." Although this doesn't seem satisfying.