The original definition is this: Castile soap is a name used in English-speaking countries for olive oil based soap made in a style similar to that originating in the Castile region of Spain. – Wikipedia
Now that term is often used to include soaps that are made with shea butter, coconut oil and palm oil, etc. as well. While not technically correct when used this way, it’s one way that people/ companies use to denote a product that is made with vegetable fats rather than animal fats.
List of castile soaps off the top of my head – ie. not comprehensive by any stretch of the imagination:
Dr. Bronner’s
Kirk’s Natural
Kiss My Face Oil Oil Soap (various scents or the plain jane variety – we use these)
Dr. Woods
Desert Essence has one as well, I believe
There are various small companies that have a line of castile soaps as well. Does that help?