if motors are electric and engines are internal combustion why is H.D. and Ford motor companies?

Obviously because Ford and Harley don't know the difference. If I would have referred to a motor as an engine while in electrical engineering I probably would have been kicked out of the class.

You correctly explain that Ford called its self Ford Motor Company.

Putting aside the discussion over electric motors V Petrol motors, A name is a name, you can call your self anything you like.

Lets consider this naming a company and what that name says. Here in Australia we have a company who makes cakes, they are called "Homemade Cakes." They display this name on the cakes. The name does not tell me that they make them at home. Its a name not a statement of what someone does.

Internal combustion is the method used with in the motor to do the task.

All that said. A motor can be an electric or a fuel powered. Electric power does not have the exclusive hold over the use of the word motor.

Yes there are other means of propelling a vehicle. Steam works but has major drawbacks. There is a sterling engine, which like the steam engine is an external combustion engine, but the rotary engine like that used in the Mazda is an internal combustion engine. Another engine that is popular in cars sold in Europe is the Diesel engine, but that is another internal combustion engine too. There are proponents for a flywheel to store kinetic energy, and when the flywheel looses its kinetic energy by slowing down you can spin it back up by plugging it in to an electrical outlet for a short time. There is talk of an engine that runs on compressed air. However if we can get the battery technology up to speed the plug in electric is the best solution on the horizon.

By definition, an engine OR motor is a machine designed to convert energy into useful mechanical motion.

A motor is a device that converts non-mechanical energy to mechanical energy. That includes electric motors and heat motors.

Both car &m/c engines are also called as motors when all the electrical components are applied

http://machaut.uchicago.edu/?resource=Webster%27s&...

Webster's Revised Unabridged Dictionary, 1913

Motor (Page: 948) n. [L., fr. movere, motum, to move.]

1. One who, or that which, imparts motion; a source of mechanical power.

2. (Mach.) A prime mover; a machine by means of which a source of power, as steam, moving water, electricity, etc., is made available for doing mechanical work.

Internal combustion engines *are* motors.

The English language was not fully developed in the early 20th century.

It goes back to the verb, "motoring", which refers to driving (or riding) a "motorized" vehicle. We don't refer to them as "engined' vehicles, do we?

Do you ride a motorcycle or an enginecycle?

One’s root is move, the other’s is ingenious.