"Do you have a tablet or a cell phone?"
Translation:Onko sinulla tablettia tai kännykkää?
"Tai" in an inclusive "or". One, some, all, or none of the options can be true.
For example, "Do you want some milk or juice?" The answer could be milk, juice, both milk and juice, or neither milk nor juice.
In Finnish, it would be "Haluatko maitoa tai mehua?"
Possible answers could be: "Maitoa", "Mehua", "Maitoa ja mehua", "Ei, kiitos."
"Vai" is an exclusive "or". Only one of the options can be true.
For example, "Is it blue or red?" The answer must be either blue or red. It can't be both or neither.
In Finnish, it would be "Onko se sininen vai punainen?".
The answer has to be either "Se on sininen." or "Se on punainen."
Here you ask, whether the questionee has any at all. In the sentence Hänellä on uusi kännykkä you describe, what the person has for sure.
While true that an adjective attribute makes in the later sentence the noun, the thing one has, more specific, it's not sufficient marker which case to select. Namely you can ask Onko sinulla uutta kännykkää?, which implies, that you know that the questionee has an old cell phone but for some reason you want to use the new one (e.g. you're holding the old one on your hand and you see that its glass surface is broken).
There are two questions that look almost identical:
Onko sinulla tablettia tai kännykkää?
Onko sinulla tabletti vai kännykkä?
The first question uses tai : inclusive or, as Jackie847172 said, and partititive object. The questioner wants to know if the questionee has a tablet or a cell phone at all. The questionee may have at his/her disposal either one, both or none.
The second question uses vai : exclusive or, and accusative object (here the accusative is equal to the nominative). The questioner wants to know which one the questionee has. The questioner has somehow already made a conclusion that the questionee has either one.
Note, because the similar expression is used to show possession Minulla on auto : I have a car, the latter usually carries an additional nuance that the questionee possesses the item, i.e. it is not just at his/her disposal.
How to express the difference in English is another matter. I would guess that the second would be "Which one have you, a tablet or a cell phone?", while the first one would remain at "Have you got a tablet or a cell phone?". Perhaps a native English speaker can better enlight this.
This article has a good summary. Note, that the end question (You have a new cell phone, haven't you) is much rarer than in English. The two examples in the article cover the most cases: a surprise or a resignation.
Edit 2020-09-12: The link address
works for me both on a phone and with a desktop browser.
Miksi nominatiivi on merkattu virheelliseksi? Itse voisin varsin hyvin kysyä "onko sinulla kännykkä?" Tai no toki "onko sinulla kännykkä?" on useammin sellainen "omistatko kännykän?" ja "onko sinulla kännykkää?" on usein "oisko kännykkää lainata?", mutta englanninkielinen lausehan ei näiden välillä erottele.
Take a look at the comments by Jackie847172 and me. There is a difference between
Onko sinulla tablettia tai kännykkää? (inclusive or; one, some, all or none of the options can be selected)
Onko sinulla tabletti_ vai kännykkä_? (exclusive or; only one of the options can be selected)
For vai there is a mnemonic vain yksi, thanks EttieNja.