ArcGIS Pro and ArcGIS Online are two different platforms with different interfaces and features. Both are licensed to current UC San Diego affiliates through our Esri License. While these two products are separate, they work seamlessly together as part of Esri's ArcGIS ecosystem of products.
ArcGIS Pro is a desktop software that is installed on Window's based computers. You can work with ArcGIS Pro in an disconnected environment. ArcGIS Pro is the desktop product that replaces the former ArcMap product. In general, ArcGIS Pro has much more capability to perform complex analysis and customize the display of your data than ArcGIS Online does.
ArcGIS Online is a browser-based GIS platform that is accessed through any browser. It is a software-as-as-service (SaaS) offering that requires an internet connection to use. Everything you do in ArcGIS Online is processed and stored on web servers, not the computer you are using to access it through a browser. In general, ArcGIS Online has much more capability for interactive and collaborative use of GIS than ArcGIS Pro does. If you want to create ArcGIS StoryMaps or ArcGIS Dashboards, you will need to have your data available in maps hosted in ArcGIS Online.
Access to either is provided by a named-user account, which is tied to your UC San Diego AD account. See setting up an ArcGIS account for instructions.