This has been rebranded as Visual Studio Online and now offers two ways to share code: The Microsoft standard Team Foundation Version Control or Git.
I’m familiar with Git as a data management tool.
You are partially correct. TFS (Team Foundation Server) is supported by Microsoft as both a cloud software product and on-premises software product. The first gets new functionality more quickly. The latter supports a wider range of functionality for integration with infrastructure. For example, if your organization uses lab environments, advanced reporting, needs work item type customizations & other customizations to your process templates then on-premises makes best sense. What TFS is in a nutshell is a product to provide practically one stop service for integrating all of your important Development/Testing/Management process data/tools in one platform. Too often organizations will be short-sighted and pick a hodgepodge of tools that are disintegrated and then they incur outrageously expensive costs for integrations, maintenance, and even more costs of lost opportunity as their processes get stymied and they aren’t agile/capable to expand & deliver quickly.
TFS is generally used by organizations that are trying to have well-integrated Version Control, Automated Builds, Manual Testing, Automated Testing, robust DevOps, solid requirements management, integration with development/process tools, and flexibility to grow & stay solid as a business.