If two people invented the same thing together (or, more commonly, one person invents feature A, and another invents feature B, where both feature A and feature B are part of one invention), then they are joint inventors (and without an assignment or an obligation to assign, they are both joint owners). On the other hand, if two people invent the same thing separately (e.g., similar research goals at two competing pharmaceutical companies), then the first to file gets the application.
It still must be an enabling disclosure, though. That is, it has to teach the public how to make and use the invention.
It still must be an enabling disclosure, though. That is, it has to teach the public how to make and use the invention.