All new resources are added as Members by default.
An Owner can configure user type in the Team & Resources tab on the left sidebar. On the right side of the user email address, there is an Act as Admin toggle. When it is switched off, it means that a user is granted a Member role. Hence, when it is switched on, a user acquires Admin rights.
Access rights for team Members can be configured for every project separately. So, for example, the same person can have a right to only work on personal tasks in one project, while having the right to edit and see the costs in another project from the same account.
For an Owner and an Admin all the rights are enabled by default for all the projects they take part in.