You're right! "Samstag" is the standard german term for "saturday". In some regions, additionally, "Sonnabend" is used. There is no difference in meaning between them. "Samstag" is understood everywhere.
As you can see on this map, "Sonnabend" is mainly used in former East Germany (and in the north): http://www.atlas-alltagssprache.de/wp-content/uploads/2012/05/Samstag.jpg
It is not necessary as it is clear that you are talking about the present day.
But of course there may be situations where you'd prefer to add the article to emphasize it. For example
you write an essay and you have to hand it in on a particular - let's say - monday. You are struggling sometimes and really want to give your best, so you mark this particular monday on the calendar to make sure you don't miss the deadline. On the monday morning you wake up and say: "Es ist der Montag." or "Es ist der Montag der Abgabefrist." (= it's the monday of the deadline.)