When you add a new Map View, the coordinate system is WGS 1984 Web Mercator (auxillary sphere) for your map. This is coming from the Basemap layer- typically the default basemap of your organization or ArcGIS Online. The first operational layer you add (vector or raster) defines the coordinate system of the Map. In my example, it's NAD 1983 Stateplane Colorado North FIPS 0501 (US Feet). By default, ArcGIS Pro applies a geographic transformation to resolve the issue. In ArcMap, this is the opposite - no transformation is applied. You are notified in a warning window and it's up to you to figure out the correct transformation method. Many customers click "Close" as they don't understand this message. I'd suggest going into your Map Properties->Transformation and see if a transformation is applied. If not, then best practice is the select the first one in the dropdown box between the "left" and "right" coordinate systems listed. See my image below: