I, too, focus on the input when talking about a differential amp.
The principle characteristic of a diff-amp is that it responds to the difference of 2 input signals; more specifically, if the 2 input signal are identical (polarity and amplitude) then there is zero output. This is why I was saying think of the diff-amp as push-pull in, push-pull out. Even more directly, if you applied the exact same input signal to both inputs (a common-mode input signal), there's zero output. A shared constant current source in the tubes' cathodes (faked to varying degrees of success by a large resistance to ground or to a large negative voltage supply) acts to force equal and opposite tube current, and so equal and opposite output voltages.
The long-tail is something of a half-hobbled diff-amp. It responds to the difference of input signals, but we typically only drive one side instead of both (ignore the feedback for a moment). The 2 input signals are still "differential" because one is tied to a.c. ground. The drawback of this arrangement is that the gain to a single output is half what that tube would normally manage; however, it does a great job of taking a single input and generating push-pull outputs (though the balance isn't perfect without jiggering). The guitar-amp long-tail then uses the un-driven input for injecting feedback, for the purpose PRR noted.