The speaker is the thing that sound comes out of. The amplifier is what controls the volume. A speaker can work without an amp, but it would only be able to "play back" at the same volume level as the sound went in. (output = imput) The amp is useless on its own. Speakers and amplifiers are used together to electronically amplify sound.
We usually talk about a TV or stereo's "speakers" whereas we talk about a guitar or bass "amp."