What this suffix does
The suffix -phobia comes from the Greek "phobos" (fear, terror) and is used to name phobias or intense irrational fears. From "claustro" (enclosed space) you get "claustrophobia"; from "arachn" (spider) you get "arachnophobia"; from "xeno" (foreigner) you get "xenophobia".
It is a very productive suffix: new -phobias are constantly being coined for modern fears (nomophobia = fear of being without your phone).
The Spanish connection: -phobia = -fobia
English and Spanish share the same Greek root. The difference is only in spelling:
claustrophobia = claustrofobia
arachnophobia = aracnofobia
xenophobia = xenofobia
acrophobia = acrofobia
In English it is written -phobia (with ph = /f/); in Spanish it is written -fobia (with f directly). The meaning is identical.
The adjective and the person
Every -phobia generates the adjective -phobic and the person -phobe:
claustrophobia = claustrophobic (adj.) / a claustrophobe (person)
xenophobia = xenophobic (adj.) / a xenophobe (person)
"claustrophobic" is the most frequent adjective in conversation: "I feel claustrophobic in the elevator".