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Which comes first, height or width?

Width comes first, then height, in most standard conventions. Windows, doors, and screens are all specified as width x height: a 3050 window is 3'0" wide by 5'0" tall, and a standard interior door listed as 30"x80" is 30 inches wide and 80 inches tall. Graphics and image dimensions follow the same rule (1920x1080 means 1920 wide). The main exception is lumber and some material specs, where thickness comes first (a 2x4 is 2 inches thick by 4 inches wide).

On floor plans specifically, height rarely appears at all, since a plan view is a horizontal slice of the building. Ceiling heights show up in notes or on elevation drawings instead. Room dimensions on a plan are width x length, both horizontal measurements.

If you're pulling dimensions from a floor plan and want to confirm what a label refers to, measuring the actual drawn walls is the reliable check. A scaled measuring tool like MeasureFloorPlan lets you verify any dimension on the drawing directly instead of trusting label order.