Hirelings are typically normal men with special skills. Hirelings typically are just hired and are effected by Morale.
Henchmen are leveled characters usually at a far lower level than the players themselves. Henchmens are recruited and are effected by Loyalty. They are typically are owed a small share of the treasure and a small share of the XP to level themselves.
Minions are just another name for Henchmen. It is used mostly for the henchmen of villain NPCs. (the folks that have the treasure you don't have.)
Retainers are the followers of name level Player Characters.
5th Edition Keep on the Borderlands, Part II
3 hours ago