It was what was called a pocket rifle, which was one of the first types of collapsible/removable stock rifles.The one that she has in particular, was marketed so that you could put the collapsed rifle into a pocket that you would have strapped to the crossbar of your bicycle.
I put a link to a blog with the actual make/model about it further down the chain.
Oh yes, it does! Not surprising she'd use different guns I guess. A little difficult to look up "Calamity Jane's gun" because it's the name of a gunseller, but Lensing the image brought up other pics of her.