"Spanish" is the modern international language that developed out of "Castillian", a medieval regional dialect spoken in the central part of Spain.
"Spanish" and "Castilian" are synonyms.
The use of one over the other depends on preference and context. There are quite a few Latin American countries today, like Colombia, Peru, Venezuela,
etc., that designate their national language as "Castilian" in their constitutions.
When I said to Fleur-de-Lys
"Castilian to be more precise," I wasn't correcting her use of "Spanish." Both terms are acceptable. It was tongue-in-cheek since all Latin Iberian languages, including Catalan and Portuguese, are "Spanish" in a deeper historical sense.