The same physics, applied in the opposite direction
Just as playback-rate changes couple speed and pitch together as a side effect, pitch-shifting has to actively decouple them in the other direction — the algorithm needs to raise or lower frequency content while keeping the audio's duration completely unchanged, which requires actually analyzing and reconstructing the waveform's frequency structure rather than simply speeding up or slowing down playback. This is technically the same category of processing as time-stretching, just solving for the opposite constraint.
Semitones are the practical unit, not percentages
Pitch changes are conventionally measured in semitones (the smallest step in standard Western musical scales) rather than percentages, because musicians think and communicate in these terms — shifting up or down by 12 semitones is a full octave, and smaller shifts of just 1-2 semitones can be used to subtly adjust a vocal recording's key without sounding obviously processed. Understanding this scale makes it much easier to dial in a specific, musically meaningful result rather than guessing at an arbitrary percentage.
Common practical uses beyond music production
Shifting a song's key to match a singer's vocal range for karaoke or practice, correcting a recording's pitch when it was captured slightly off from a reference (a common issue with older analog tape transfers where playback speed drift affects pitch), and various voice-effect applications for content creation all rely on this same underlying capability, just applied toward different ends.
Where the algorithm starts to show its seams
Like time-stretching, pitch-shifting handles moderate changes (a few semitones) cleanly but introduces audible artifacts at extremes — a large upward shift can start to sound thin or robotic, while a large downward shift can introduce a muddy or warbling quality, because the algorithm is reconstructing frequency content it doesn't have direct data for at those distances from the original. Staying within a modest range produces the most natural-sounding results.