The distinction between hirelings, followers and henchmen always seemed frustratingly nebulous in Dungeons and Dragons.
It didn't help that original Dungeons and Dragons allowed you a certain number of hirelings, based on your Charisma, while AD&D changed the terms, provided you instead with a certain maximum number of henchmen. You could be excused, then, for conflating the two classes of non-player character, or at least finding the issue sufficiently confusing to dispense entirely with the process of retaining hangers-on.
Then there was this whole business of followers. Adding a third category of NPC to an already crowded field of fellow-travellers didn't help matters.
Thankfully, that much maligned 2nd Edition Advanced Dungeons and Dragons rule-set came to our rescue (or if you prefer, continued to chip away at the glorious obtuseness of the original D&D rules).
The 2nd Edition Players Handbook (pages 114-115), now and forever, put an end to any questions about the nature of those three types of NPC's.
Hireling: A hireling is a person who works for money. Hirelings are always employed for a stated term (length) of service or for the performance of a specific task. Hirelings do not serve a PC out of great loyalty.
We played it that you could retain as many hirelings as you liked, within the confines of how many you could afford, were available and willing to work for the party (particularly an issue if the players developed a reputation for returning from an adventure, sans hirelings).
Follower: More reliable than those who are motivated purely by money, followers are drawn into service by the reputation of the player character. Followers serve only those with significant power and reputation, thus the construction of a stronghold is necessary to attract followers.
We played it that you only attracted followers at "name" level, after you had built your castle, chapel, thieves' guild, and so on.
Henchmen: Henchmen are adventurers who serve out of loyalty. Although they expect their share of treasure, (ie. they get treasure and therefore xp) they do not usually join a player character for money. They are attracted to the PC because of his reputation ... therefore, henchmen cannot be expected to flock to the banner of a neophyte adventurer. A PC's Charisma determines the maximum number of henchmen he can have. This is a lifetime limit, not just a maximum possible at any given time.
And that's the way we approached the issue of Henchmen. If you were allowed a maximum of 5 henchmen, and all of them died, you could not attract any more. We were more lenient however if the henchman left your service, having reached the same level as the PC.