Open source: anyone can use, study and modify it, including businesses. Free: no cost, but the code is closed. Freemium: a lasting free plan with paid tiers for extra features. Source available: code is public but the license adds conditions.
FAQ
What is the best free alternative to Microsoft Project?
The most popular picks are ProjectLibre, GanttProject, OpenProject and Plane. To open .mpp files and build Gantt charts the way MS Project does, use ProjectLibre. For team collaboration on the web, use OpenProject.