http://www.circuitstoday.com/wp-content/uploads/2011/11/PiezoTransducer-Circuit-Symbol.jpg
http://www.circuitstoday.com/wp-content/uploads/2011/11/Loudspeaker-Circuit-Symbol.jpg
I have generally found it useful to give a picture along with an explanation - it makes the jargon more grounded, pun intended.
Top picture is a Piezo (crystal) transducer symbol. In the simplest of terms, bend a crystal, it will emit electricity. Apply electricity to a crystal, it will bend. But, as you may see from the symbol, there is no direct connection between the two poles of the transducer.
A magnetic speaker, whether PM or Field Coil uses a voice-coil that is moved by changing AC voltages applied to the voice-coil. So the two poles are directly connected via the voice-coil. Yes, there is DC continuity - and as a rule, magnetic speakers do not like DC.
That the tube tester wants magnetic headphones indicates that it is a low current output device. Given that most tube testers - pretty much a done-deal after the 60s by way of design improvements - have no formal amplification built in, a magnetic headphone makes more sense. What the "Noise Tester" is measuring is a sample from the anode load resistor and amplifying the output to a speaker (or eye tube) - depending on the manufacturer.
Some testers have settings for this test that more resemble actual operating conditions, rather than "full throttle current" as typically done for life-test.
The above few lines from "sample" through "Life-test" are quotes.
http://www.john-a-harper.com/tubes201/#Noise
However, there are all kinds of noise - usually in very small values.
Peter Wieck
Melrose Park, PA