For clarification - regardless of what online sources and dictionaries currently reckons, and I reckon they're wrong -- the actual definition of piano comes from 'piano forte'. People in the past simply wanted a keyboard instrument that has keyboard notes tuned in the same pitch sequence as our modern instruments, with independent note sound level control for each note -- the soft-loud (aka piano forte) quality. They didn't really care how it would be done. They didn't care about approach. They just wanted something, and wanted it done.
So a piano is any keyboard instrument that has that feature. And can even throw in sustain/damper feature for extras.
So even a synth keyboard having percussive string sort of sounds are pianos, as are digital pianos. Hybrids are pianos too, and hybrids are in fact digital pianos. They just need to have various names to try distinguish the features and applications of these various pianos. Acoustic pianos are obviously pianos. So all of these instruments - having sound level (velocity) control for each individual note independently - are pianos.
Hence the two categories - acoustic pianos and digital pianos. They're all pianos.
Sure - for many digital pianos, a design 'intent' is to aim toward making particular (digital) pianos sound more or less like acoustic pianos. And regardless of whether somebody wanted to design the digital piano to work toward reproducing features of acoustic pianos (or not) -- we know that digital pianos are indeed pianos. Emulation of acoustic piano. Sure. That's fine. But - a digital piano is a piano. That's final.
Also - anybody that reckons that it's necessary for sample-based digital pianos to be based on sampled acoustic piano sounds -- well -- I reckon that they're mistaken. People could indeed build a system that has the bulk of acoustic piano parts - but without pedal, and without 'key mechanisms' - and just get electro-mechanical parts to do the striking and dampening - and have mics and sampling equipment take samples. In that case, the digital piano won't actually be based on sampling an 'acoustic piano'. The development of these digital pianos won't require an acoustic piano to become realised. It would just be one possible approach toward digital piano development.
And - these days - as can be seen and heard -- digital piano music is impressive. Very impressive. And for many music - or heaps of (actually unlimited amount of) acoustic-piano sounding music, the music from digital pianos is actually second to nothing. This doesn't take away from acoustic pianos. As the music from acoustic pianos is also second to nothing. The two categories of piano are equal. One category is not better than the other when doing overall (broad range) features and applications comparisons.