I wonder if it is rootstock. Most roses are grafted onto a rootstock
(because they are breeding for color, not roots).

Sometimes it can take over the original rose (especially after 20
years). You can usually tell by the small red roses, and sometimes
the leafs are smaller than normal too. Usually they only bloom once a
year.

They're still perfectly fine roses, they just might have a name. And
they may actually have a SMELL!

All roses bloom on new wood, so it's best to prune in winter or early
spring. You can prune now to remove dead wood or stray canes, but
nothing too drastic. And give it a little 1/2 strength fertilizer.
Good luck