Unlike in pretty much all other countries in the World, Israel separates Nationality from Citizenship and there are more rights on the latter than on the former.
Further, uniquelly in the World Israel has different kinds of Citizenship such as Israeli Jew Citizienship and Israeli Arab Citizenship and the former has more rights than the latter.
As with every other piece of hasbara propaganda, those massive bollocks you're parroting are a meaningless façade for external consumption that hides the reality of a State were Apartheid is so deeply entrenched that by law non-Jews have a second class kind of citizenship with less rights than Jews who have a different class of citizenship.
They're both said to be Israelis (as there is but one nationality) and if one ignores all the rest they're both as you say "Israel's citizens", they're just de jure different kinds of Iraeli citiziens with different rights and, as I said in the beginning, most rights there are linked to Citizenship, not Nationality, so for example Israeli Arab Citizens can be denied the right to live in certain places whilst Israeli Jew Citizens cannot.
And to preempt the usual hasbara response to this disclosure: those Arabs don't live there because it's such a great situation, they still live there even though they are second class citizens because they've always lived there as they were born there on what was their family's land before it was stollen from them.
This idea of a difference between nationality and citizenship is admittedly new to me. Can you provide a citation to a reputable source that explains it in more detail?
Israelis are not alone in using propaganda, so a neutral source, preferably. Or the law itself, I can run it through a translator.
Actually I was a bit wrong (I had been told this by others but only research the details now to provide you with references) so here are the corrections:
First I had it the other way around - it's the nationality that has Jewish and non-Jewish, not citizenship. Specifically Israeli nationality is only for Jews and it's for any Jew independently of were they are born source
Second, it's not all Arabs that are discriminated by law when it it comes to citizenship, it's only some who, although born in the territory of Israel are seldom given Israeli Citizenship when they ask. This applies not only to the occupied territories in the West Bank and Gaza but, more shockingly, Jerusalem source. This is why once in a while you get news of Arabs being evicted from their houses in Jerusalem: they were never actually given Israeli citizenship even though they were born in Israel and if they apply they are unlikelly to get it as per Israeli law they have no right of birth to it.
And then of course there are plenty of sources refering to Israeli Arabs being treated as second class citizens, such as this Bloomberg article
PS: I also remembered how some of the details I listed above, such as how Israeli Arabs can be refused license to live in certain places, came from a Documentary I saw on TV years ago. If I remember it correctly it's done via a scheme which is a bit like "housing associations" but for for larger areas (towns?) were people have to apply to them to be allowed to go live there and in many places Israeli Arabs are simply never accepted so they can't go live in those places.
That Haaretz article is saddening. I cannot in good faith blame Israel for not giving citizenship to people who do not want it and don't apply for it, but reading some of the excuses they gave for denying applications is telling.