When sharing tasks or entire plans with teams and individuals, access rights can be set :
A reader can see the properties of a task, but not edit them. She cannot see its permissions.
An editor can change, add, and delete tasks. She can read permissions, but can't edit them.
A manager has free access and can edit everything. She can edit permissions and place new ones.
Of course, roles can be changed later on and permissions can be removed at any time.
Get to know your responsibilities
The owner is a particular person managing access rights. When changing the ownership the old owner gets read access to this object.
A person being the responsible for a task automatically gets Editor rights to that object. But note that only persons having access to the project can be set as responsible.