If projects are owned by the team, anyone on your team can access them. If projects are owned by you, your team does not have access. Only users you invite to collaborate on your personal projects can access them. This way, you can keep your personal projects separate from your team projects. You can check who owns the project by viewing the members section in the bottom right of the project. Personal projects are specified with "Owner" next to the user who owns the project; team projects will specify "Owner" next to the team name.
You can also distinguish between your personal projects and your team projects by navigating to your general homepage or team homepage (top left). Your general homepage "Home" displays both personal and team projects - your team projects indicated by your team avatar you uploaded or the default avatar assigned to your team. Your team homepage only displays your team projects.