No difference really, Simon is right in that some, particularly the main manufacturer, Shimano, have designed their "Up" trigger shifter to change up only one gear at a time, but allow either one, two or three when changing down by how far the "Down" trigger is pulled.
When a twistgrip shifter is used, how many that are changed is up to the rider's amount they twist the grip, but if trying to change up more than one, it will only happen if it's done slowly. Don't worry, you won't break anything by getting it wrong, it will just refuse to change smoothly so you'll know what was wrong.
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