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What do you mean by "downloading maps directly from OSM"? OSM is a database.

If it is downloading rasterized images from the web site, then the difference is that Organic Maps is a vector mapping app.

I think it's using downloads from https://download.geofabrik.de/ That extracts regions from Open Street Map and packages them as files.

What if their format changes? The app will no longer work.

It is fairly standard source for OSM data afaik. Organic Maps uses it as well at least for some cases.