The music theory is the same, and of course the key layout and the notes are the same. If you are thinking of a digital piano with tones like Rhodes pianos and organs, it's virtually identical to playing a piano.
But if you get into synths, there are potentially new techniques to learn and different ways to think about things. These probably aren't things you spend years studying with a tutor. It's just a matter of being creative and willing to experiment with and adapt to the number of sounds available to you. For example, you could be playing a string melody with your right hand, and your left hand might be using controls to change the amount of vibrato or bend the pitch on certain notes. Some synths have a monophonic style where only one note at a time will make sound, and you can do interesting things like having the pitch slide from note to note. Some sounds take time to develop, so then you would want to play with a slow style and not a bunch of running scales. There might be functions where you hold down a chord and the synth turns it into a preplanned arpeggio sequence. And of course, the ability to design your own sounds is a completely different world.