In Spanish "castellano" means what we call the Spanish language, in English. The word is used in certain countries more, like Argentina and Spain. In Spain, it is used to contrast with other national languages, but it includes non-Northern dialects like Andalusian.
In English, "Castilian" or "Castilian Spanish" refers to the dialects of Spanish spoken in Northern Spain. It has the theta sound. So people are always asking me about "Castilian Spanish." The presence of this sound is not a "lisp." That would be like saying that someone who pronounces "math" as "math" rather than as "mass" is speaking with a lisp!
Spanish in the New World took the Southern Spanish dialects as its basis, so the theta is unknown. Aspiration of d (intervocalic or terminal) is common both in Andalusia and the Caribbean. So "to" and "na" instead of "todo" and "nada." Also aspiration of s before a vowel or in terminal position. ¿Cómoetáuté? There are other phonetic differences, like "yeísmo," the pronunciation of ll as y.
There are 500 million speakers of Spanish, and the language has quite a global reach.