The difference between Carriage and Coach

Carriage as a noun:

The act of conveying; carrying.

Carriage as a noun:

Means of conveyance.

Carriage as a noun:

A wheeled vehicle, generally drawn by horse power.

Carriage as a noun (British):

A rail car, especially one designed for the conveyance of passengers.

Carriage as a noun (now, _, rare):

A manner of walking and moving in general; how one carries oneself, bearing, gait.

Carriage as a noun (archaic):

One's behaviour, or way of conducting oneself towards others.

Carriage as a noun:

The part of a typewriter supporting the paper.

Carriage as a noun (US, New England):

A shopping cart.

Carriage as a noun (British):

A stroller; a baby carriage.

Carriage as a noun:

The charge made for conveying (especially in the phrases carriage forward, when the charge is to be paid by the receiver, and carriage paid).

Carriage as a noun (archaic):

That which is carried, baggage

Coach as a noun:

A wheeled vehicle, generally drawn by horse power.

Coach as a noun (rail, UK, Australia):

A passenger car, either drawn by a locomotive or part of a multiple unit.

Coach as a noun (originally, Oxford University slang):

A trainer or instructor.

Coach as a noun (British, Australia):

A single-decked long-distance, or privately hired, bus.

Coach as a noun (nautical):

The forward part of the cabin space under the poop deck of a sailing ship; the fore-cabin under the quarter deck.

Coach as a noun (chiefly US):

The part of a commercial passenger airplane or train reserved for those paying the lower standard fares; the economy section.

Coach as a verb (intransitive, sports):

To train.

Coach as a verb (transitive):

To instruct; to train.

Coach as a verb (intransitive):

To study under a tutor.

Coach as a verb (intransitive):

To travel in a coach (sometimes coach it).

Coach as a verb (transitive):

To convey in a coach.