Hair is the strands that grow on your head and body; a hare is a fast, long-eared animal related to the rabbit. Memory hook: hair is what you brush, while a hare is what you see darting across a field.
The core difference
Hair is what grows on skin, while a hare is an animal (and, as a verb, means to run very fast).
- hair — the strands growing on a person or animal: She dyed her hair a deep shade of red.
- hare — a long-eared, long-legged animal like a large rabbit: A hare darted across the field.
- hare (verb) — to run very fast: He hared off down the street when he saw the bus leaving.
How to tell them apart
The two words sound identical, so the mix-up only shows up in writing. Ask yourself whether you mean something on a head or something in a field. If it has fur and ears, it is a hare; if it can be brushed, it is hair.
The idiom by a hair (a tiny margin) uses hair, not hare, because it means a single strand. The verb to hare, meaning to run very fast, is the only other place you will meet the animal's spelling.