Plate and spring reverbs are in some ways very similar devices but they are quite different in sound. A plate reverb is a thin sheet of metal, suspended via springs (or sometimes clamps) under tension inside a rigid frame. A transducer (similar to the voice coil of a speaker) is used to vibrate the plate, and then contact mics on the surface of the plate pick up the vibrations. The wash of delayed reflections as they bounce around on the plate creates a reverberant effect that can be mixed back in with the dry signal. Plate reverbs tend to sound very dense and bright, which makes them good for vocals and drums. Plates are quite large, and tend to be used in recording studios.
A spring reverb is simpler than a plate reverb, but similar in concept. One or more springs are held under tension in a “tank.” A transducer vibrates the spring or springs, and a transducer pickup captures the reflections as they bounce back and forth along the spring. Spring reverbs tend to produce twangy and percussive reverb effects, which can sound fantastic for guitar. This is why many guitar amps still use spring reverb mechanisms today, though spring reverbs have been used for studio and other sound applications as well.
Today, “real” plates are out of production, but there are myriad choices among plug-in and hardware reverbs for authentically recreating the effect. Spring reverbs are widely available in guitar amps, and many plug-ins and hardware reverbs offer realistic spring reverb emulations.