Hard rays often called spines, and differ from the soft or blunt rays.
Certain anal fins contain 3 or a more spines, the rest soft, and counting each separates some genera or species from another
Some examples.
Vieja have 13 spines in the dorsal, and 16 soft rays in the dorsal,
In Cinelichthys, pearsei has 13 spines, while bocourt has 14, and in similar species the spiny or soft ray count helps distinguishe one from another.
If you have a taxonomic key for Cichlasoma these differences might be spelled out, and may be the only way to tell them apart, without knowing anything else about them, like catch location.
Just looking at a fish is not reliable, unless you count all hard and soft rays. This is why ID questions answered on a forum are most difficult and often unreliable, unless a photo clearly showing a count is obvious.