No, I believe facet is simply referring to the location of the injections. "Medial Branch Nerve Blocks" is the proper medical terminology (and probably the better google search phrase). Facet block is probably just faster to say. I'm pretty sure the medial nerves innervate more than just the facet joints. I believe facet joint inflammation is often secondary to degenerative disc disease. From my cervical facet blocks it felt like I got relief in the scalenes, SCMs, and levators.

Definitely something to talk to your doctors about to better understand. My understanding is likely incomplete.