Personal plans are meant for individuals working on their own projects and collaborating with others. For maps owned by a personal account, you can only add people to your map as collaborators (meaning they have edit access).
Organizations allow multiple users to manage a central account, along with additional branding opportunities, team management, and fine-grained access control to projects. For maps owned by an organization account, you can add people to your map using a powerful team-based structure with either view, edit, or admin access.
Both personal and organization accounts have a free tier which include an unlimited number of public projects.