You've discovered that "matched" doesn't have one definition, like the word quality.
Mu is defined, gm is defined.
My experience, with a balanced mono block, push pull output, is that when I matched the output tubes in the amp, clarity and depth increased a little. In this amp, a 6FQ7 is used as a cathode driver. If I changed the driver, the "match" changed. To match the tubes, I adjust the a variable resistor common to both tubes, so that the output voltage is the same.
I have about 30 output tubes, and will go thru many trying to get two that "match".
I have three different testers, one just for common small signal tubes. This one measures the db gain of each triode-something I can relate too.
I've measured my hearing, not matched.
I measured the room "gain" at my listening position from each speaker, also not matched at the test frequencies.
One time, I bought 250 Tungsram E88CC. I sold the tubes with gain matched triodes and gain matched pairs and use unmatched triodes and unmatched pairs.
One time, I bought around 30 mi surplus 6SN7GTA, identical tubes. Some were boxed 7 years later than the first boxed date--they all sounded the same.
Best
Bob