In a long-tailed pair formed using bipolar junction transistors, the emitters are connected together, and then through a resistor or constant current source to ground. In this form, one of the transistors can be thought of as an amplifier operating in common emitter configuration, and the other as an emitter follower, feeding the other input signal into the emitter of the first stage. Since a transistor will amplify the current flowing between base and emitter, it follows that the current flowing in the collector circuit of the first transistor is proportional to the difference between the two inputs. However since the circuit is totally symmetrical, either element can be viewed as an amplifier or as an emitter follower, understanding does not depend on which role you assign to which device.
Long-tailed pairs are frequently used in circuits that implement linear amplifiers with feedback, and in operational amplifiers.