A test manager is one who
-
manages a collection of test leaders
-
is the leader of a test team or teams
-
gets paid more than a test leader
-
reports to a test leader
A test manager is defined as the leader of a test team or teams, responsible for planning, monitoring, and controlling test activities. This role is distinct from a test leader (who might manage a specific project or subset of tests), and involves managing people, resources, and the overall test strategy rather than just executing tests.
A test manager is correctly defined as the leader of a test team or teams — per ISTQB terminology, the test manager role owns test planning, strategy, resourcing, and reporting for one or more test teams, distinguishing it from a test leader/lead who may manage a single project's testing. "Manages a collection of test leaders" is too narrow/specific (a test manager's scope isn't limited to only managing other leaders). The pay and reporting-direction options are irrelevant organizational trivia, not definitions of the role.