Evade and elude overlap when someone escapes a pursuer, but evade is usually a deliberate act, as in evading a question or a duty. Elude also covers things that slip from your memory or understanding, such as a name that eludes you.
The core difference
Evade is usually about deliberately avoiding something, while elude can also describe something escaping your memory or understanding.
- evade — to cleverly avoid a person, question or duty: He evaded the reporter's question with a joke.
- elude — to escape, or to fail to be remembered or understood: The meaning of the poem eluded most of the class.
How to tell them apart
A useful test: you evade a question or a duty, but a name or an idea eludes you. If the thing being avoided is a person or a chase, either word can work, as in The suspect evaded police or The suspect eluded police.
The difference shows up most when the subject is not a person. A cure, a word or an idea can elude you, as in A cure has eluded scientists for decades. Evade points to someone choosing to avoid something, so it fits deliberate dodging of questions and responsibilities best.