What is the difference between tests that confirm the correct operation of the system and tests that check its incorrect operation or errors?

Tests that confirm the correctness of the system (positive tests) verify that the system behaves according to requirements under correct input and conditions. They ensure that functionality is implemented correctly.

Tests that check for incorrect operation or errors (negative tests) aim to verify the system's robustness against erroneous or non-standard situations — for example, incorrect input, failures, or exceptions. They help ensure that the system handles errors properly and does not break.

Example in Java with JUnit:

@Test
public void testValidInput() {
    assertEquals("OK", system.process("validInput"));
}

@Test(expected = IllegalArgumentException.class)
public void testInvalidInput() {
    system.process(null); // expecting an exception
}