Clarendon is a variation on the 19th-century slab serif, AKA antique, but with bracketed serifs. Ionic is an older term. Many revivals bearing the Clarendon name have been released by various foundries. Uses are tagged with this generic entry unless a specific revival is confirmed (see Related Typefaces).
“Though technically a 19th-century innovation — Figgins included brackets on a set of capitals in 1833, Caslon followed with a bracketed lowercase in 1844, and Benjamin Fox produced the first face called Clarendon for the foundry of Thorowgood and Besley in 1845” — Hoefler & Co.
The Clarendon we know best today is Hermann Eidenbenz’s 1953 adaptation for Haas.