Hi, Cosmas,
Yes, they are both translations of Michael.
Μιχαήλ is the Christian name given at baptism, Μιχάλης is the informal nickname, think of Mike.
There is also another nickname for Μιχαήλ: Μίκης, but quite rare, in fact I only know of one Μίκης, the great deceased composer Μίκης Θεοδωράκης.