ArcGIS Pro
When you use ArcGIS Pro, login using your ArcGIS Online ID or your ArcGIS Enterprise ID. You will automatically be able find and use to all the content you have access to. The online help details how you can search for and use data from your Portal. Therefore, provided the service has been shared with the user and/or they are members of the correct groups they will be able to use the service.
ArcMap
When using ArcMap users should login to their ArcGIS Online account or ArcGIS Enterprise account through the file menu and selecting ‘Sign In’. Full details of signing to ArcGIS Online or your ArcGIS Enterprise portal in ArcMap can be found in the online help. Certain services will be unavailable in ArcMap for instance vector basemaps.