Re: "Matching" transformer.
I think you have virtually answered your own questions!
Speaker isolation transformer - to provide isolation from a live chassis item to an external speaker. (Many of these won't meet current safety standards, but almost certainly nobody has died yet as a result of insulation failure).
Matching transformers would match, say, a 15Ω loudspeaker to an amplifier designed for 3Ω. Impedances in common use are 3Ω, 8Ω, 15Ω but there is also the 100V standard where a matching transformer might be used to match an 8Ω speaker to a 100V line at 10W.
The output transformer in your valve amplifier is of course a matching transformer, but to avoid confusion it would probably be referred to as an "output transformer" rather than a "matching transformer."
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