The meaning of these two terms depends on the data being examined:
In a per-meeting context, the Unique Participant is the entity that took part in the meeting, no matter how many times she or he joined and left. In the same context, any call into the meeting will count as a Participant - for instance:
A meeting takes place between 8 parties - there are therefore 8 Unique Participants. During the course of the call, two parties dropped their connections, and rejoined. There where therefore 10 Participants but still only 8 Unique Participants.
Data Covering a Time Interval
When dealing with data specified by a time interval, the term Unique Participant refers to each party seen once or more times during the interval
Participant, however, refers to the total count of parties (whether repeated or not) over the time interval.