Attendee: Someone who is at an event such as a meeting or a course.
Participant: Someone who is taking part in an activity or event.
Longman Dictionary of Contemporary English
Participant can have a more exclusive meaning than attendee. It suggests that the person is being more than present, they are actively participating.
In some contexts, they might have the same meaning.
For example for a conference:
For both of these, we mean everybody who attended the conference receives the gift bag.
In other contexts, 'participant' might have a more exclusive meaning.
For example at a marathon:
This suggests that supporters and watchers of the marathon also were entitled to the free hotdog.
Suggests that it's only the people who ran in the race that were entitled to the hotdog.
An attendee is there, but they may not be participating: they might be asleep, or otherwise uninvolved.
A participant is active.
Practically speaking, I believe these words are interchangeable. To get more technical, one could perhaps consider someone attending an event but not actively participating to be an attendee, but not a participant.
First, some rough definitions:
Attendee = one who was there for the event
Participant = one who did something during the event.
There's a certain sense of mere attendance in the word attendee that makes it so some contemporary events prefer to think of all present as participants. Here, I take it the basic idea is that even if you don't have a specific role, you participate through active listening.
Conversely, some events maintain a strict distinction between attendee and participants. Say for instance, a panel discussion in front of a 1000 college students. In such a case, the participants are all the people on stage, and the people watching are attendee.
To make the point in a different way, I explain to my students that I grade participation not attendance. By which I mean, if you come to class and sleep, you did not participate. If you come to class and play on facebook or stackexchange, you did not participate. But you did attend. (This is especially relevant for students in the Japanese education system where it was classically the case that you could pass by attendance )