Is there a term for a noun that is the "-er" form of a verb?
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?
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?
The suffix is called an agentive suffix, and such words are also often called agentive as well.