Elude means to escape or avoid something, or to fail to be remembered or understood. Allude means to refer to something indirectly. A name might elude you, but you allude to a story without naming it.
The core difference
Elude is about escaping or slipping away from someone; allude is about hinting at something without saying it directly.
- elude — to escape or avoid, or to not be remembered or understood: Her name eludes me right now.
- allude — to refer to something indirectly: He alluded to the problem without mentioning it by name.
How to tell them apart
Try this trick: allude starts with all, and you allude to something, so it always points at a topic. Elude starts with e, like escape.
The mix-up shows up in writing because the two words sound close. Remember that elude is about something slipping away from you, while allude is about a hint. Also note that allude is normally followed by to, whereas elude takes its object directly.