Sure, can be. Some high-end digitals ape a real piano as much as possible, with wooden keys, a wooden case... Cheaper models often use wood in the "furniture" part of their structure.
If you want a distinction, I think you'll have to look at methods of sound production rather than materials.
A piano has hammers that hits strings and relies on a soundboard to reinforce the sound.
An electric piano still has a mechanical action where a key is pressed, something gets hit. Then amplification and speakers take over. What is hit may be similar to a tuning fork (Wurlitzer, Rhodes) or may even be a set of strings (Yamaha CP70) - which is where the distinction between electric piano and real piano can become blurred. If you want to call the CP70 an "amplified piano" I'm not going to argue too hard!
Electronic piano is an analogue synthesiser voiced to sound like a piano. Digital piano is a sample player with piano sounds. These two categories can also overlap. Either may be equipped with a keyboard designed to feel like a piano action. But ultimately it ends up operating a switch, not hitting something that makes sound directly.