The difference isn’t that much. Asteroids are the rocky/metallic bits that were left orbiting the Sun after planet formation. Comets typically come from interstellar space or have highly elliptical (high eccentricity) orbits periodicity paying a visit to the inner solar system. They tend to have lots of ice and when the Sun heats them up you get the signature tail.
Thats the key difference. If you look around the classification in astronomy you tend to encounter things that are labelled differently but aren’t that different. (Think of asteroids and meteors, technically a mateor is something an asteroid does.) This is mainly because astronomers discover and classify things based on how they look on the sky or throw a telescope so sometimes they end up giving a special case of something a different name. Still comets are rock, metal and ice like most asteroids but the tail, now that looks pretty distinct.
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