Thanks for posting to the community site. We offer our products in both open source and professional versions. The open source products are licensed under the AGPL (Affero) licensing agreement. We cannot provide legal advice or interpretation of the license but would suggest that you work with your legal counsel for guidance. That said, many corporate users do indeed use our open source products.
Our professional products (RStudio Connect, RStudio Workbench (formerly RStudio Server Pro) and RStudio Package Manager) are licensed under a commercial license agreement. The full agreement can be found here. They include numerous features that are particularly useful for enterprise deployments including performance management capabilities, monitoring and administration, and commercial support. If these products are of interest, please let us know and we can provide more detail. In addition, we offer our desktop product under a commercial license if needed. Information can be found on the products page of our website here.
I'd be happy to discuss on a call as well and can message you privately to find a time that works well. If you ever have questions for the sales team, you can contact email@example.com as well.