There’s actually an absurd amount of terminology for pronunciation, and it applies to many many languages, including rhoticism. Some of the most common terminology for R sounds are things like alveolar trill, tap, or flap, uvular trill, fricative, and approximant, retroflex approximant, bunched R, tapped R, flapped R, apical R, vocalized R, ect ect. And this is just for some possible R sounds. Many of these aren’t talked about as much by English speakers as Rhotic vs non Rhotic R sounds because a lot of these aren’t that present in the most well known English dialects (you won’t get trills in most forms of American, British, Canadian, or Australian English), and because some changes are harder to notice (to Americans, rhotic vs non rhotic Rs are easier to notice than bunched Rs vs alveolar tapped Rs, just because many would assume alveolar tapped Rs are a D or T sound rather than R). You get this stuff for all the sounds found in languages around the world, which makes it super interesting, but also hard because of the sheer amount of terminology there is for phonetics