In NAE, ‘trapezoid’ is the shape with at least two parallel sides, and a ‘trapezium’ is a convex quadrilateral with four unequal sides.
Elsewhere, it’s the other way around.
The word trapezoid is actually the older way of calling it, dating back to the 5th century; using ‘trapezium’ dates back to the 16th. (See here)
(Edited to streamline this comment about three years after writing it)