Every e-piano is a synthesizer!
The difference between a keyboard and an e-piano: keyboards mostly have smaller keys, piano-keys are wider.
A good piano-action has a weighted hammer action and in case of Rolands even cheap models already: also escapement. Together that means that hitting the keys feels not like a home organ or keyboard, but an accoustic piano. Keyboards usually have keys that are "on or off", and feel completely different from those on a piano, they offer no dynamic. I would always go with an epiano, therefore. You can switch the keys to keyboard action, if you want (no dynamics, just on and off).
The sound characteristic of an e-piano's piano voices can be completely tuned and manipulated as if you where tuning a real accoustic piano to the demands of a professional pianist. At least the Rolands.
Roland is market leader for e-pianos, if you go for one, check them first. Roland also is THE great name in electronic music creation, they are market leader and pioneer. There is no way around them.
E-pianos can be set to "synthesizer" sounds as well, e-pianos, different accoustic pianos, natural sounds, effects, and so forth. The one I use has 370 voices! However, I stick to pianos, I am a beginner, cannot virtuously play a musical orgy on that thing. But its also nice to know there are a good jazzy bass when playing with split keys (bass on letf hand, piano on right hand...), or nice mellow sounds to combine one keystorke with two vopices: say a typical 80s e-piano and some mellow strings, giving you that typical Whitney Houston music style. And the French akkordeon makes me melting away in bitter-sweet melancholy...
I posted some videos above introducing the instrument I got. I am EXTREMELY HAPPY with it, have only good things to say about it. And the keyboard action is sensational, I cannot differentiate it from a piano. Onboard sound via speakers is 2x11W, that is marking above its price range.
However, I post another video on Roland, so that you know why you do not want to miss them out. The prices for their FP keyboards I find very fair.
I would ALWAYS opt for a model giving you blutooth MIDI for sound input and for data (that is two things). It nicely combines with a tablet, for notes, for software of any kind. I can, however, also use a Midi cable. Blutooth is the exception from the rule in this price range below 1000 coins.
If you are more new than experienced, two more features I found very worthwhile to make use of: the metronome is easy to start, because when practicing as a beginner, my tempi are all over the place. And the record and replay feature, very useful. when you learn a piece, you usually learn left hand first, then right hand, and then you put it together somehow. You can record one hand and then practice the other hand to the sound of the first. Easy to use, very useful.
Incredible bang for the buck:
https://www.roland.com/global/products/fp-30x/
A word on headphones. They need to match the power output of the source. Phones with high Ohms will not get loud if being used on a small MP-3 player. Phones with low Ohms will explode if being connected to a stage amplifier. For the keyboard I use, anything in the range of 35-45 Ohms should work allright. And the difference between consumer and studio/monitor headphones. The latter are being used for production, and there you have a need to not add anything to the sound of the given instrument in recording, nor take away anything from it. You want a neutral and realistic sound, only then the sound engineer who mixes the sounds can assess how good the used settings are. Thats means these headphones, moiitors/studio, sound very flat and thin when you listen to a full orchestra, I do not like their sound at all, its terrible - BUT: when using such a phone on a single keyboard only, it is brilliant! Thats why I have two headphones now: one for the keyboard, a monitor for 35 Euros, again by Roland, and a fuller, complexer phone for actually listening to music from orchestra. The differences can be extremely immense, do not underestimate them. I am happy with the Roland RH-5, its specs seem to match the keyboard's output well. Phones with more Ohms than this seem to not make every keyboard player happy, I read.
On Roland company and why its e-pianos are so good. They do some important details differently... The moderator obviously is a salesman, but he hits valid markings. The E-piano of my parents is a Yamaha, it has a better key action than home organ or a keyboard synthesizer, but it feels not as real as mine. The smaples used also are n ot as good. So, there are differences even within the same price segment.
Via app I can also use many effects and accoustic background noises, from natural sounds like flowing water and wind to machinery, explosions, rotors, weapons, etc. Even laughter. I like the applaus. The library has around 370 entries, only 56 of these can be accessed directly from the keyboard, for the rest you need an app.