I 100% understood everything you typed before you typed it...Red Dragon, Manhunter, Silence of the Lambs, and Hannibal all center around Hannibal Lector. All four movies are connected even though there are different actors playing the central character.
Desperado takes the story from El Mariachi and moves it forward, same character, different town, and it has callbacks to the first flick but it replaces Carlos Gallardo with Antonio Banderas in flashback scenes, particularly the one where he get's shot in the hand by Moco (fun fact: Carlos Gallardo WAS actually in Desperado, but he played one of the other mariachi's Campa, the cat with the machine gun guitar case)
So, they're all direct sequels. A better example of a spiritual sequel would be Gross Point Blank and War Inc. or Blade Runner and Soldier.
I just asked is something a true sequel if none of the actors are reclaiming their roles.
I don't think so.