Great question, I’ve always assumed armature/skeleton to be the same thing, here’s a quote from an animation Wiki page;

“When sculpting the human figure, the armature is analogous to the major skeleton and has essentially the same purpose: to hold the body erect.”

Source : 

and another from a Skeleton animation Wiki page;

“A rig is generally composed of both forward kinematics and inverse kinematics parts that may interact with each other. Skeletal animation is referring to the forward kinematics part of the rig, where a complete set of bones configurations identifies a unique pose.”

Source : 

and finally, a quote from Blender’s manual;

“An “armature” is a type of object used for rigging. A rig is the controls and strings that move a marionette (puppet). Armature object borrows many ideas from real-world skeletons.”