To sum up, the first is the answer when having a "yes or no" question. As for the second, it is the usual way to talk about how often sth happens, or to mention the day of the week in which we do/take/ or whatever sth (that structure with this meaning, you see, can be applied for any day of the week).
From my point of view, it is not about the correct way. They are different, see:It is Saturday
= é sábado
What is the best day of the week?
I guess it is Saturday.
Which day is after Friday? (lame question, but still right
it is Saturday.it is On Saturday(s)
= é no sábado
, aos sábados
How often do you study English?
On Saturdays. (Aos sábados)
It is on Saturday that I can really be part of the forum.
On Saturdays I do lots of things.
It is pretty common to use "on" when talking about days, but not necessarily using "it is"