Some states originally defined "mopeds" by displacement, max speed and pedals. Then when 49cc scooters became more common, the pedal requirement was dropped for "mopeds" in some states to simplify licensing details.
Since the OP is in Texas,
here's how that state sees it:
Texas specifically defines a "moped" as:
A motor driven cycle whose speed attainable in one mile is not more than 30 miles per hour and that is equipped with a motor that produces not more than two-brake horsepower. If an internal combustion engine is used, the piston displacement may not exceed 50 cubic centimeters and the power drive system may not require the operator to shift gears.
Further, Texas issues, for people without a driver license of any sort, a "Moped Driver License" for which one only need take a written test. NO driving skill test is required for this restricted license. Our grandson received his "moped license" on his 15th birthday, the day he became eligible.
So, no matter what any of us may call a Honda Metropolitan or any other 49cc scooter, the Great State of Texas, as well as many others, legally define it as a "MOPED".
Al