The team-managed project type is managed by the project administrators, allowing the team to determine and execute changes without the need for assistance from the Jira Administrator. Project administrators also do not need to be concerned about interfering with other projects because team-managed projects do not use Jira schemes and operate independently.
The company-managed project type is managed by your company. Essentially this means that only the Jira Administrator can perform changes that impact company-managed projects. If your team needs to work across multiple projects in a standard way, have a complex workflow, or need a detailed permissions scheme, you should choose the company-managed type.