Original: Traditionally, the bony fish had been treated as a class within the vertebrates, with Actinopterygii and Sarcopterygii as subclasses. However, some recent works have elevated Osteichthyes to superclass, with Actinopterygii and Sarcopterygii as classes.
Simplified: Osteichthyes are a taxonomic superclass of fish, also called bony fish that includes the ray-finned fish (Actinopterygii) and lobe finned fish (Sarcopterygii).