Electric Piano vs. Synths?

Absolutely. Electric pianos and organs (and even the Mellotron) are mechanical in nature, not electronic...there's not much difference between an electric piano and a guitar, both use the pickup microphones to take a quiet sound and send it to an amplifier; the tone of the device still depends on the physical components. There's some flexibility (like organ drawbars and tone knobs and such) but you still have a basic unchanging 'real' sound source to work with.

Synthesizers are basically just fancy electronic buzzers; the sound is generated from basic electronic waves and subsequently altered through circuitry. The tone of the instrument depends only on how the circuit (real or computer-modelled) is designed and how creative you get with the settings. With flexible (and/or more numerous) circuit routings, the possibilities of even a basic primitive analog synth (such as the Minimoog) are staggering.

Virtual synths are even one step beyond that, in that the 'circuit' (or even the 'mechanics') are computer-modelled to behave any way you like. A modelled Minimoog doesn't have to worry about the limitations of mid-70's analog circuits, and a modelled electric guitar can be made of granite and have a neck twenty feet long if you want.

Clavinets are more related to harpsichords than pianos, but the basic principle is the same: when you press a key, a hammer ('striker' for the Clavinet) hits a string, causing audible vibrations. Like an electric piano or guitar, the Clavinet has built-in pickup microphones to amplify the sound.

What makes a Clavinet so unique? The strings (more like electric guitar strings than piano wire, lots of percussive attack but very little sustain), the 'strikers' (rubber rather than wood or metal) and the biggest humbucker pickups I've ever seen, with a very unique design and response. The Clavinet is also more responsive than many electromechanical keyboards, allowing for wide variations in tone depending on your playing style.

Plus, they really get the most out of effects (overdrive, wah pedals, phasers, etc.) because their tone and output is comparable to electric guitars, which the vast majority of effects were designed for.