If I tried different time signatures, I still heard the same. Why? How are different time signatures active? Also by default I didn't have 2/4. Last choice was custom, I inserted 2/4 there. Now 2/4 is the last choice and my list of signatures starts from 3/4... Video is included. https://youtu.be/T6PgFp69_kM

I think you are confusing Time Signature with Tempo. Changing the Time Signature will not change the sound of the music, it's just a way of determining how the musical beats are grouped (where the bars start, where the accented metronome clicks fall). The course attached above explains -- look at video #6 to start..

Time signature changes the sound of music - 3/4 is waltz, 2/4 is march... And they are completely different...

No, the Time Signature you set in GarageBand doesn't change the sound of the music -- YOU change the sound of the music if you play along with the metronome/click at a different Time Signature, following the groupings/accents of that Time Signature. But notes that have already been recorded/entered into a Region won't change in any way just from you changing the Time Signature after the fact -- as you heard. The Time Signature in GB (or any DAW) is a guide for the player/performer to create a new musical part, not an editing function for an existing musical part.

What means "following the grouping/accents of that time signature" ? What are they and how can I follow them?

When a musician records a musical part on a track in a DAW, he listens to the metronome click and plays along with that, using those regular clicks as a reference so the notes he plays/records will be in time with the bar/beat ruler in the DAW. The metronome clicks represent beats, which are grouped together into a repeating pattern called a bar (or measure), with an accented beat (click) followed by several unaccented beats (clicks). The pattern of accents is based on the Time Signature -- so in 4/4 time, there will be 4 beats (clicks) in each bar (each group of metronome clicks), one accented beat (click), the downbeat, plus three unaccented beats (clicks), the rest of the beats in that bar. Musical parts/rhythms are played along with the metronome clicks -- this makes it easier to play/record multiple tracks and keep them in time with each other and with the DAW bear/beat ruler. If the musical parts (notes) are in time with the DAW bar/beat ruler it makes it easier to make musical edits like cutting and re-arranging Regions or quantizing notes for tighter musical timing. To explain music theory properly really requires audio examples, which cannot be included in a text-based discussion group. I encourage you to watch the recommended videos -- I've attached a different course to this thread -- watch the 1st video and then skip to video # 6 and watch (& listen ) from there for a fuller explanation of how music theory of rhythm applies to DAWs: https://www.macprovideo.com/course/music-theory-109-music-theory-for-daw-musicians?afid=E470KLQ7r9 And here's the link to the previously-attached music theory course, in case you neglected to bookmark it: https://www.macprovideo.com/course/musictheory103-rhythm?afid=E470KLQ7r9