The tune written out for your instrument, or moved into another key
Many band instruments are “transposing”: when a B♭ clarinet plays a written C, out comes a B♭, a tone lower. So to sound in the same key as the fiddles and whistles, its part has to be written a tone higher. An E♭ alto sax sounds a major sixth below what's written, so its part goes up a major sixth, and so on. Folk tunes are nearly always written at concert pitch, which is right for fiddle, flute, whistle, concertina, melodeon, guitar and the rest.
“Into another key” is for everything else: a tune that sits too high to sing, a whistle in a different key, or a set where the next tune wants to be in G.
The ranges used for the warnings are the comfortable range of a typical instrument; good players go further.