Is the Sabbath Saturday or Sunday?

The simple answer is, "Yes!"  
Now the longer answer:   To the Jewish people, the Sabbath day was Saturday.  Sunday was the first day of the week.  They still celebrate the Sabbath beginning on Friday at sundown.  

When Jesus rose from the dead, we are told that He rose on the first day of the week.  "For Christians is has become the first of all days, the first of all feast, the Lord's Day ... Sunday:  We all gather on the day of the sun, for it is the first day ... when God, separating matter from darkness, made the world; and on this same day Jesus Christ our Savior rose from the dead."  Our celebration of Sunday fulfills the commandment to observe the day of worship.  It follows the rhythm and spirit of w weekly celebration of God, Creator, Redeemer, and Sanctifier.  (CCC 2174 & 2175) 

However, we Catholics allow for a vigil on the Saturday night before to be considered as the Sunday Mass.  ... I think this might come from the fact that the Jews consider that a day starts at sundown.  They get this idea from the Creation story in Genesis.  "Evening came, and morning followed - the first (second, third, etc) day."

Incidentally, a Mass said the day before cannot count as the next day's Mass unless it begins at 4:00pm or later!  ... Oh, so many details!!

To summarize the answer your question, it depends on whether a person is viewing the Sabbath from Jewish or Christian perspective.  Than, it depends on whether you are talking about the evening vigil prior which must be at 4:00pm or later.