A Motion Tween animates symbols moving in space; when you create a motion tween, then you can click on any frame in the tween, move the symbol on that frame, and watch Flash automatically build a motion path animating the frames between that frame and the next keyframe. Any frame where you’ve manually moved the tweened symbol becomes a keyframe.

A Classic Tween works the way old motion tweens used to, in Flash CS3 and earlier. In this kind of motion tween, you’d have to manually create all your keyframes and connect all of them with motion tweens that followed point A to point B.

A Shape Tween performs distortions on non-symbol shapes/vector graphics. If you create one shape on one keyframe and another shape on another keyframe, you can connect those two shapes with a shape tween. The tween will perform whatever calculations and morphs needed to transform the first shape into the second.

A shape tween is a transformation tween, while a motion tween/classic tween affects position, rotation, and transparency.