Delete
Mode
Edit Mode
Menu
Armature ‣ Delete ‣ Bones
Hotkey
This tool delete selected bones, selected joints are ignored.
If you delete a bone in a chain, its child(ren) will be automatically re-parented to its own parent, but not connected, to avoid deforming the whole armature.
Dissolve
Reference
Edit Mode
Menu
Armature ‣ Delete ‣ Dissolve
Hotkey
Ctrl-X