A royalty interest entitles a mineral owner to certain payments from a lessee if oil & gas are produced from his/her property or from a unit of which his/her property is a part.
Sometimes a mineral interest owner assigns a non-participating royalty interest in a tract to another party. That party will then have a right to receive royalties under any lease covering that property if oil & gas is produced, but they will not have the right to execute a lease themselves.
On the flip side of things, sometimes a lessee assigns an overriding royalty interest in a particular lease to another party or reserves an ORRI when assigning a lease. The party holding the overriding royalty interest will then have the right to receive royalty payments during the life of the lease if oil & gas are produced. Once the lease expires, so does the ORRI.