What do you call a clock that has a minute hand and a hour hand?

It's an analog clock.

The BIG hand tells which hour you are in because an hour is the bigger unit of time measure and the minute is the smaller unit. The little hand tells what minute of the current hour you are in. Granted, most analog clocks have one longer hand and one shorter hand but they are correctly referred to as BIG for hour and LITTLE for minute. Think about it, function over form. Don't be a sheep, this is the original reasoning behind the size and shape of the hands.