If you have a metal box, there should be a grounding pathway to the metal box. This can be a ground wire attached to the box with a #10-32 screw in the threaded hole provided on the box; or metal conduit (but not necessarily armored cable); or a combination.
A receptacle has a set of metal ears on top and bottom. This is called a "yoke". These metal parts are bonded internally to the ground socket holes and the ground screw.
If you have a grounded metal box... and the receptacle is screwed down so that the ears bottom out on the metal box... and you have solid metal-metal contact between receptacle and box... that is a valid grounding path. It is not valid if the ears "hang up" on drywall or plaster and there's a bit of screw length. Despite being all metal, screws are not a valid grounding path.
Two breakers, two circuits
Imagine if you unfurl 500 feet of electrical wire parallel to a high tension line. Will you get a measurable voltage? You bet. You're picking it up like radio waves. Will it be useful for anything? Nope.
The same happens in wires running parallel in your house. If one is hot and you test the other, sensitive voltmeters like a DVM will see a stray voltage. It's not useful for anything; an incandescent night-light won't light up. In fact, that's a great way to arrest this stray voltage: plug a night-light into one receptacle while measuring the other.
Other than that, I would say you have a very serious problem if the socket measures 120V with one breaker on, and 0V with both breakers on. That would indicate something complicated and weird, and potentially dangerous.