The short answer
A sound is a wave, and its pitch is how many times that wave repeats each second. Speed the whole recording up and every repeat arrives sooner, so the pitch rises with the speed. There is no way to separate them: on a record, speed and pitch are one control.
A video player does not speed the recording up. It cuts the sound into short pieces, plays each piece at its normal speed, and overlaps the pieces so the words take half the time. Inside a piece nothing was squeezed, so the wave repeats at the rate it always did and the voice keeps its note.
On a record, speed is pitch
Vinyl makes this obvious because the mechanism is visible. The groove holds the shape of the wave, and the needle traces it at whatever speed the platter turns. Turn the platter twice as fast and every wiggle in the groove arrives twice as often, which doubles the frequency of everything on the record. Doubling a frequency is exactly one octave.
Disc jockeys live with this, and their equipment admits it: the slider that changes the deck speed is labeled pitch. One slider, both effects, because the machine cannot give you one without the other.
What a video player does instead
Playing a video at 2x uses a different method, and the goal is the opposite one: keep the pitch, change the duration. The player chops the audio into short pieces, each a fraction of a second long, and plays every piece at its ordinary speed. Then it slides the pieces closer together than they started, overlapping them, until the whole run takes half the time.
Nothing inside a piece was stretched or squeezed, so a wave that repeated 120 times a second still repeats 120 times a second. What was removed is the time between pieces rather than the time inside them. That is why a sped-up lecture still sounds like the lecturer, just impatient.
Why the pieces have to line up
Overlapping two pieces of a wave is only free when the two agree about where they are in their cycle. Butt a piece that is halfway up its wave against one that is halfway down and the two partly cancel at the seam, which is heard as a click or a wobble running through the sound.
So the player does not drop each piece where the arithmetic says. It nudges the piece a little in time until its wave matches the piece before it, then lays it down. Done well, the seams disappear.
There is a limit, and you can hear it. The player can only line the pieces up against one sound at a time, and it picks the loudest one. In a talking video that is the voice, so the voice comes out clean while music underneath, which has its own cycles and does not agree with the voice about where the seams should fall, can wobble. The artifact is not a bug in the player; it is one decision being made for two sounds.
Keeping the speed and moving the pitch
Run the same machinery with the opposite setting and you get a voice changer. The tool that stretches time without moving pitch can also move pitch without stretching time, and a pitch shifter is the second case: your words come out at their normal speed on a different note.
In Patchd the Pitch Shifter is one of the Studio voice-fx nodes. Its Pitch dial runs -24 to +24 semitones, and it carries a second dial, Formant, from -12 to +12. That second one matters here: a record made you higher and smaller at once, because squeezing the wave moved your resonances along with your note. Raising Pitch alone leaves your resonances where they are, so you get the note without the shrunken body. Raise both by twelve semitones and you have rebuilt the record, deliberately, at your normal speaking speed.
Which dial does which is laid out in formant shift vs pitch shift, and helium is the same split happening to you in a party balloon.
The takeaway
Speeding a recording up multiplies every frequency in it, so a record at 2x is an octave higher and a voice turns into a chipmunk. A video player at 2x cuts the sound into short pieces, plays each at its normal speed and overlaps them, so the words take half the time while the note stays put. The pieces have to be lined up against one sound, and that is why music under a sped-up voice can wobble while the voice sounds fine.
Patchd is a Windows audio mixer with a full effects rack on every channel, and the Pitch Shifter with its separate Formant dial lives in the Studio voice-fx rack. It is in open beta now, and if you clear the terms your invitation arrives straight away. The Studio tier is $5.99 a month, $39.99 a year, or $119.99 once for a lifetime license, and the real-time engine is identical on both tiers.