While you can grant read/write access to collaborators on a personal repository, members of an organization can have more granular access permissions for the organization's repositories.
A repository owned by a user account has two permission levels: the repository owner and collaborators. For more information, see "Permission levels for a user account repository."
Organizations manage membership with teams. There are four levels of access available to members of organization teams: Owners, admin access teams, write access teams, and read access teams. Except for Owners, team members only have access to the team they are in and the repositories assigned to that team. For more information, see "Permission levels for an organization repository."