Does it usually happen even if all of the adviser's students have very different research interests?
These meetings can serve a variety of purposes, but many of them fall into the broad category of keeping the adviser and all the group members updated on what everyone in the group is doing. Below are some of the secondary benefits of a group meeting:
- saves the adviser time (compared to meeting with students individually)
- motivates the students to keep doing work, so they have something to report at the meeting
- fosters a sense of community with the group
- provides the students experience giving informal presentations
- often leads to the more senior students mentoring the junior students
To answer your follow-up question in the description, no, some faculty meet with each student individually; in fact these separate meetings are common, for example, in mathematics.