score:3
Try the app “GPS Navigation (Sat Nav)”. It uses OpenStreetMap, and the maps are available offline (one country map is included in the price of the app, you need to pay extra for additional maps, currently it’s $10.99 for the whole world). You can tap a location on the map and get directions for going there, with different options for driving, walking or cycling (works offline too). You can view the directions as an overview map, or as a moving map that follows you and gives turn-by-turn directions, including the remaining distance. The app recalculates the directions automatically if you’re wandering off. One quirk the app has is that you may still get messages about the need for an internet connection, even if you turned on the “offline” option in the app; but the maps and directions do work offline.
You might also want to try Pocket Earth (free), it also uses OpenStreetMap and allows downloading the maps for offline use (requires an in-app purchase, currently $5.99 for the whole world). It can offer navigation directions, though you need to be online for it to calculate a route, which you can then save for offline use. If you wander off, it’s limited to warning you about it if you’re offline, it can only recalculate the route if you’re online. See the section “Routes & Navigation” in the Pocket Earth Help Manual for details.
There’s a table of iOS apps on the OpenStreetMap wiki, including details on the navigation features of the apps. The above two apps are the ones from the table I’m familiar with and which offer some navigation features. Perhaps another app more closely matches the feature set you’re looking for.