The original navigation software used routing software and navigation map data from Navigon/Garmin.
The new navigation software is evidently using maps from Mapbox and Valhalla's routing software (Valhalla was acquired by Mapbox).
NAV 1.0 displayed Google road and satellite maps on the console display and used the offline navigation map database for routing and for display on the dashboard.
If the console display for NAV 2.0 shows "Google" in the lower right corner, then Google maps are still being used for the console display. If the Google logo is gone, then the console maps must be from another source, which might be the offline navigation map database (which seems unlikely, due to the size of the satellite data).
Since we haven't received the update on either of our Model S cars yet, can't verify this ourselves - yet...