As far as we know, there is only one tesseract in existence, and this is that tesseract. If there are two, doesn't that kind of throw of Thanos' grand plan to collect 'em all? There's never been mention of a second, which means the one Mar-Vel is using is the same one that's been around the galaxy multiple times.

Is the Tesseract and the casket the same thing?

The Casket of Ancient Winters belongs to them and it came into the possession of Odin, who stored it with his other powerful objects like the Tesseract.

Did the Frost Giants have the Tesseract?

The Tesseract ends up on earth because it was lost during the battle between Odin and the Frost Giants. During Thor we see Thor talking (as a child) about how he wants to wage war on the Frost giants, like his father (Odin). So we know that the Tesseract must have been lost already.