No, FOSS apps are completely free. You can download the entire OsmAnd code from https://github.com/osmandapp/OsmAnd and compile it yourself if you are so inclined. Some developers choose to restrict features for FOSS apps distributed on Google Play though.
If you want "OsmAnd+" and "Maps+" features, download it from a FOSS source, like F-Droid and get:
Maps+
• Unlimited map downloads;
• Topo data (Contour lines and Terrain);
• Nautical depths;
• Offline Wikipedia;
• Offline Wikivoyage - Travel guides.
OsmAnd Pro
• Cross-platform;
• Hourly map updates;
• Weather plugin;
• Elevation widget;
• Customise route line;
• Online Elevation profile.
This has nothing to do with an OsmAnd subscription though.