Team Foundation Version Control (TFVC) is a centralized version control system. Typically, team members have only one version of each file on their dev machines. Historical data is maintained only on the server. Branches are path-based and created on the server.
Azure DevOps Server, formerly known as Team Foundation Server (TFS) and Visual Studio Team System (VSTS), is a Microsoft product that provides version control (either with Team Foundation Version Control (TFVC) or Git), reporting, requirements management, project management (for both agile software development and waterfall teams), automated builds, testing and release management capabilities. It covers the entire application lifecycle and enables DevOps capabilities. Azure DevOps can be used as a back-end to numerous integrated development environments (IDEs) but is tailored for Microsoft Visual Studio and Eclipse on all platforms.