A:
Technically, they mean roughly the same thing, but they usually have a somewhat different feeling.
"one of ours" (which is short for "one of our people/agents/workers/etc") says "a member or representative of the same organization as us" or "somebody who is working for us". It has a feeling that that person is working on behalf of the same group, but is not closely associated with the speaker within the organization (they are a member of a different team, or a subordinate, or somebody who mostly works on their own, etc).
"one of us" says "part of our group / organization / family / etc, exactly the same as we are". It has more of an inclusive feeling of considering that person to be the same as them and part of the same close-knit team or group (and they would defend and support them the same as themselves, etc).