Literally, none. But νιπτήρας is the bathroom's sink, where one washes oneself (νιπτήρας comes from νίπτω which means wash). Νεροχύτης is the (kitchen's) sink where one spills water into (νεροχύτης is νερό+χύνω = water+spill) to wash plates, vegetables etc.
Yes, ένας νιπτήρας" is a wash basin as you'll find in a bathroom to wash your hands. Ένας νεροχύτης" is the kitchen sink.
Here's a Greek proverb: το 'να χέρι νίβει τ' άλλο και τα δυο το πρόσωπο "one hand washes the other and the two the face." And "Νίπτω τας χείρας μου" (Pontius Pilate) This means "I'm not responsible." "I wash my hands of it."
The quote from Pontius Pilate is quite common in Bulgarian as well („измивам си ръцете“), but it is normal for anything even barely connected to Christianity to be similar in both languages.
The first one is a part of one of the most beloved children's songs in Bulgaria, which roughly translated into English means:
Hey little hands, hey those two!
They listen to me the most, woo-hoo!
The one washes the other, and both – the face!
It is such small things that made me fall in love with Greek! :)
νίβω and νίψη are used for purify and purification accordingly, nowadays.
In greek το 'να χέρι νίβει τ' άλλο και τα δυο το πρόσωπο "one hand washes the other and the two the face." means that "one person helps the other and together they work for a common goal"
νεροχύτης --> kitchen sink νιπτήρας --> bathroom sink where you wash your hands
χύνω ( https://en.wiktionary.org/wiki/%CF%87%CF%8D%CE%BD%CF%89 ) is a verb meaning to pour or flow.
χύτης is a noun derived from that verb meaning something like a "pourer" -- one who does the action of the verb.
So a νεροχύτης is a "water pourer", literally -- the place where water flows down.