It is a small but important distinction; I say it isn't public because the the moderator doesn't have to let "the public" into the meeting, such as those non-voter visitors. Only registered voters and a few select town/school employees are required by law.

In a regular public meeting (at least in MA, where the state Open Meeting Law governs public meetings) you simply can't do that, you must let everyone in, even random tourist visitors who just want to watch. Town Meetings are not under open meeting law, they have their own laws (in fact two chapters of state laws).

I've been to Town Meetings in maybe ten towns, and as part of a job a friend has been to several dozen. The moderators are always happy to welcome guests, but (for example) the auditorium in my own town is small enough that the moderator sometimes does not let visitors in until it is clear there will be enough space for all voters first. Perfectly legal, but if the selectmen did that for a selectmen's meeting (a public meeting), it would be an open meeting law violation.