What is meant by the "lead end" of an electric motor? Is it simple the end of the motor where the leads exit? If so, what does it mean if there is a wiring box centered on the motor?

Motors have a place to make connections, I usually see them on the end of the motor, It doesn't matter, it needs wiring where ever the connections are.
Some motors can be wired for 2 speed, high or low voltage, and reversed, depending on how you connect.