Thank you for your question!
RStudio Server Pro - Very similar to the Desktop IDE, but runs on a server. This is very helpful for a few reasons: it allows you to have more compute resources closer to your data, it provides a uniform environment for teams that makes it easier to collaborate, and it provides controls for administrators to monitor and scale work.
RStudio Connect - Makes it easy to share R Markdown reports, deploy shiny web applications, and deploy APIs written in R. Connect can also be used to share Jupyter Notebooks. Whereas GitHub stores your code statically, RStudio Connect knows how to run it, which means your work can be accessible to non R users. For example, a user can visit a shiny application on RStudio Connect and interact with the app without ever knowing R code is involved! Likewise, you can have RStudio Connect run reports on a schedule and send emails with the results.
Our team would be happy to chat further about the differences, or show you a demo. Alternatively, you can try our Quickstart VM or take a look at beta.rstudioconnect.com.