Quality is delighting customers
Usually, when a tester starts his testing session, he begins to with a specific target in mind. He begins with identifying the test case and ends with eliminating the bugs and the defects found. This is not the case when the tester is going for an exploratory session.
For these exploratory sessions, the testers usually conduct an exploratory testing which is a form of black-box testing.
The exploratory testing technique is all about detection, examination and education. It emphasizes chiefly on the individual freedom and accountability of every individual tester. Test cases are not planned or created in before the qa testing but the testers check system on the random basis. The test cases are not pre-defined but are defined during testing. It is about the improvement of test design. It is like an investigation of a system or an application. it typically uses session-based test cases.
I completely agree with you that For these exploratory sessions, the testers usually conduct an exploratory testing because Exploratory testing is a meticulous investigative practice.
It is test design and test execution at the same time. This is different from other test cases, they are not pre-defined and are not carried out as per any plan.
It might be confused with ad-hoc testing as well, which is an improvised form of bug detection.