If you are talking about the one that is visible from the road, it is AL32, Terrell Cave. I think the other one you are talking about (at the bottom of a small pit) is AL39 King School Cave.
This is according to the ACS map, which shows both caves on the same map. There is some confussion as to which cave is Terrell, and which is King School. According to some accounts, the names are mixed up from the original, historic names. These accounts suggest that the cave near the road is actually King School Cave, and the other one is Terrell Cave.
Guntersville SP has a few other small caves here and there. As far as them "advertising" this cave- heck, they might as well, since it is within sight of the main road.
PM me if you need more info.
Trogman