Good question! Firstly, the name they used is the same. In Hebrew Most High God is "elyon" and it's used in both verses you refer to.
Melchizedek is a really interesting character. In Psalms 110: 4 there is a bit where it says "you are a priest forever, in the order of Melchizedek". But who is this "priest forever"? The writer of Hebrews gives the answer, at 5:5,6 and I encourage you to read that book (it's in the New Testament) to clarify this answer. In short, the forever priest is Jesus of Nazareth. His God is the God of Abraham, Isaac and Jacob (Matthew 22:32 and elsewhere). And he is the "priest in the order of Melchizedek". So the God of Abraham and the God of Melchizedek is surely the same.