Sometimes the tests are sufficiently inaccurate that you have to use a number of them to give you the best chance of making the right diagnosis. You can either use them serially or in parallel. You use them serially in an emergency room perhaps and will admit the patient if any one is positive since the disease is so serious or life threatening. Or you use 2 tests in less exciting circumstances and again treat the patient as having the disease if one or both are positive.
When you do tests in parallel you do a test, wait, and do the other. If you do this, for whatever technical reason, always do the test with the higher specificity first, if you can, because you will have fewer false positives to test with the second test (and will save money).