Is there a term for a noun that is the “-er” form of a verb?

Question

Is there a term for a noun that is the "-er" form of a verb?

For example, one who races is the "racer", and the one who writes is the "writer", so "racer" and "writer" can both be classified as what kind of noun?

Answer 1

The term is agent noun.

The endings "-er", "-or", and "-ist" are commonly used in English to form agent nouns.

For further insight, see e.g. this question: What's the rule for adding -er vs. -or when nouning a verb?

Answer 2

The suffix is called an agentive suffix, and such words are also often called agentive as well.