Turntables have a fader which controls the speed of the rotating vinyl. This fader is used by DJs to synchronize the tracks between two or more turntables before they mix the tracks together. I know that in general the term 'pitch' stands for the height and lowness of a sound. So why is it called pitch-fader when it has the purpose to adjust the speed?
I know that in general the term 'pitch' stands for the height and depth of a sound.
Hmmm... not really! Pitch is the name we give for subjectively how high or low an audio frequency sounds. And frequency is a measurement of how many times per second something is vibrating - or, you could say, how fast it is vibrating.
When you turn the record faster, the needle will go over the little vibrations in the record groove faster, so you will get more of them per second, increasing the frequency and pitch. (Of course the audio on a typical record is a mixture of many different notes at different pitches, but speeding up the record will increase the pitch of all those different notes together).
In other words, pitch and playback speed are pretty much directly linked, at least with traditional analogue technology. As Tim says, there are some digital tricks that can be used to vary speed and pitch independently, but they involve complex processing of the audio.
Because a DJ might be adjusting the speed in order to align the tempos of two songs, or he might be doing it to align their pitches. Changing the rotational speed will do both.
Using a computer, we can adjust tempo and pitch independently. With an analogue turntable they're linked. Faster will also be higher.
But don't expect the labels on consumer electronics (or even professional electronics) to always stand up to strict technical or semantic scrutiny!
With a turntable for vinyl, changing the speed at which the record turns will inevitably change the pitch of the song. Slower speed means lower pitch. Yes, its action is to adjust the speed, but the reaction is to adjust the pitch. People listening will pick up on a pitch change more readily than a slight speed change. So, whilst it's a bit of a misnomer, it's what it is. Digitally, as with CDs and later stuff, tempo can be adjusted keeping the same pitch, and/or pitch can be adjusted while keeping the same tempo.