Some Tennessee CS units suffered many name changes at times but here's probably your connection-
Four company's of Murray's 4th Tennesee Cav. were incorporated into Baxter Smith's 8th Tennessee Cav., aka Smith's 4th Tennessee Cav., when the 4th(Murray's) was disbanded in Jan. 1863
Co. C from Sullivan County became Co. B
Co. H from Smith County became Co. C
Co. I from Hamilton County became Co. H
Co. F from Fentress County became Co. I

So he could actually have belonged to both the 4th Murray's and the 8th(4th) Baxter Smith's