Your research has brought you to the Buteyko Method. You may be wondering about other techniques and what are the differences.
Pranayama - breath control in yoga
Tummo - from Tibetan Buddhism
most talked about:
Wim Hof the "Ice Man"
strangest-sounding: is it a Japanese martial art? sounds like "potato"
Buteyko Breathing Method
Then there is ... box breathing, coherence breathing, soma, conscious breathing, art of living, mindful breathing, holotropic, tantric, rebirthing, inner fire, and more! ...
You could be instructed to:
breathe fast, breathe slowly, breathe shallowly, deeply
big breaths, small breaths
hold your breath
don't hold your breath!
breathe more, breathe less, breathe through your nose, through your mouth,
quietly, loudly ...
Wow! It can't all be right? Can it?
Well, perhaps ... given the right circumstances.
It depends on the technique, the effects you're looking for, how you are and even who you talk to!
The techniques are neither right nor wrong. They might even work together!
I recommend James Nestor's book "Breath" for a fascinating read about breathing techniques where he joyfully and thoroughly explores history, effects of, protagonists - it's a wonderful read.
and back to, the Buteyko Breathing Method