“Hostage” implies a criminal. It suggests Hamas is an organization such as the “Mafia” (which at this point in time probably should not be capitalized). It also means that Israel can execute them after a brief trial, but can not attack civilians or infrastructure in retaliation (just as if the local drug pushers live next door, you can’t blow up the building and everyone in it).
“Prisoner” implies a government. It suggests that Hamas is the lawful government of Gaza (they did win the last election), and its forces and the armed forces rather than a gang of terrorists. This means that their kidnapping civilians violates the Geneva Conventions (which apply to official armies, not criminals).
If Hamas is the genuine armed forces of a largely independent state, it makes things much more awkward for almost everyone.