As the name suggests, release events are to commemorate some kind of release. In the underground circuit it is usually a CD. In other cases it can be photo-books or DVDs. But I would say that 99% of release events are CD release events.
These are events that are done by one group only. They will be the only act and thus try to fill an entire (larger) venue by themselves.
One-Man shows are really special for groups. As I said in the section about multi-group events, most if not all groups in the underground circuit start out at multi-group events. The default in the industry is usually that they have zero fans to begin with because they're only starting out. So they need to gather fans at events people might have attended for other acts.
When a group gathers enough fans to be able to hold a one-man live it means that they have reached a major milestone. Not all one-man lives are big, some might start on a smaller scale but being able to just stand in front of their own fans only is a big moment for a group.
One-Man's are usually lives (aka concerts). They might involve smaller portions dedicated to something else (talk) but the main portion will be the live performance.
Sometimes One-Man shows will be held for a special occasion, for example to commemorate the group's anniversary or as the 'final' lives of a group before a hiatus or disbanding.
The difference between a Tandoku and a One-Man is that One-Mans are more 'official' than Tandokus and usually bigger in scale. This means that there won't be cover songs for example but only group original songs. A Tandoku might also be more loosely organized. Tandoku Events are also not always lives. They can also be talk events or the groups can do a multitude of things that don't always include singing or dancing (e.g. theater performances, comedy skits, playing games, etc.).
Fan Meetings are essentially Tandoku events that focus more on, as the name says, meeting the fans. So the performance or live portion might be significantly shorter than the 'tokutenkai' following it but this is up to the group to decide. Sometimes there is no big difference, and sometimes there is. And in some cases, the admission to the event is limited to a certain group (aka fans only) but again, it is very flexible.