A joint, which is a "full" license, allows the person to possess it, store it (assuming they meet the security requirements, etc), and do everything the "owner" does. A training license only allows the person to use the gun under the fully licensed person's supervision, but they cannot possess it on their own, store it at their house (assuming its separate to the fully licensed persons house), etc.
The key point to remember is that licensing is not related to ownership in gun terms. In other words a license is not proof of ownership. An Gardaí don't care at all, or as much, about who owns the firearm only that the person in possession of it is licensed to possess it.
If someone is filling out an FCA1 for a licence to jointly use a gun which i own and am licenced for, what do they fill in as the "source" of the firearm?
Is it a) Me b) The original RFD or private source from which I initially purchased the firearm c) N/A or d) Something else?