What do we call a person who believes in god but not in a particular religion?
To begin with, there are many ways to describe “a person who believes in [G]od” (or gods). Believer, theist, etc., can be used when the context already makes clear which particular god(s) are meant, or when it does not matter. When you also want to identify the god(s), you can often find a particular word, such as Christian for a person who believes in Jesus Christ.
Then there are many ways to describe a person who does not believe “in a particular religion”. If the person does not believe in any religion, they are unreligious or not religious. If you mean a particular religion, you can often construct a description using not or non, such as: non Muslim or not Buddhist. (In a noun phrase, these will generally be hyphenated, as in: “non-Jewish Israeli”.)
To identify both in a person together becomes more of a puzzle. Depending on your needs, you might try the popular “spiritual but not religious”, or something like “non-sectarian Christian”. Or, if you are describing the person from the point of view of the religion they don’t believe in, heretic, apostate, or atheist.¹
- The word atheist was coined by believers as an epithet for a person who is estranged from the gods or abandoned by them, and is still used in that sense by believers to mean a person who rejects their religion: Gk. atheos "without god, denying the gods; abandoned of the gods; godless, ungodly". (Online Etymology Dictionary) Atheists themselves adopted the word much later.