The ability musical practice runs on
Playing in an ensemble requires continually matching your pitch to the other players, and that adjustment is a judgement of distance. Reproducing a melody by ear is faster when you trace intervals than when you route each note through its name. Transposing an accompaniment works once chords are understood as combinations of intervals. That music theory is built on relative descriptions — scale degrees and chord symbols — reflects how central this ability is to the work. Absolute pitch can serve as an auxiliary, but it is not the foundation music rests on.
How it responds to training
Relative pitch is reported to improve with training in adulthood, and this is where it differs most from absolute pitch. Repeatedly comparing two notes teaches you where to direct your attention, and judgements grow finer. Reading that improvement as a gain in the underlying ability calls for caution: whether the benefits of cognitive training carry beyond the trained task has been debated for a long time, and most reports find the transfer limited. A rising score is best taken first as evidence of familiarity with the task.
Why it suits measurement
Relative pitch is also convenient from a measurement standpoint. Play two notes at the same loudness and timbre, varying only the pitch, and the judgement of which is higher barely depends on the frequency response of the speakers or the volume setting. Attempts to measure absolute sensitivity instead produce results dictated by the hardware. Keeping the notes within the range of ordinary speech ensures that even a device's built-in speakers reproduce them reliably.