I think it is renamed to distiguish the paid play store version from the free f-droid version which is technically the same app.

I found this commit with name changing.

But no further clarification, only:

Clarify osmand naming

Dated: 29.08.2012 at 12:32.

know for sure but my guess is that the + version is the paid version on play store with unlocked features. Since this is the full free version on fdroid they changed the name to clarify the difference.

Edit: Found on Wikipedia under licensing that this does seem to be the reason. https://en.m.wikipedia.org/wiki/OsmAnd

Osmand+ is the paid play store version, Osmand~ is the open source version. I believe there’s no significant differences.

I’ve been wondering this for a long time too actually. Perhaps the name was taken?