The enhancements made in 7.6.4 on the map side are related to the mobile fist removal. The communication between ArcGIS and the Apps are now made without mobile first.
There were also enhancements on the offline map data preparation in Map Manager and also we introduced the usage of spatial indexes in the queries of the offline map data. This last one gives more performance when map data is displayed in offline mode.
Hello Dianne,The online map is based on map/feature services from ArcGIS and you can display other attributes using it. The offline map uses TPK for the basemap and ArcGIS Map Replicas for the dynamic layers.
The following playlist contains some videos about it.