Originally bikes didn't have gears, you turned the pedals once and the wheel turned once and the size of the bicycle gear depended on the size of the wheel on the old "penny farthing" bike.
Then bikes evolved and had pedals, chain rings, sprockets and chains, so you could have one gear at a time, if you wanted to change you could stop and turn the rear wheel round and have a different gear on the other side of the hub and you had the choice of a freewheel or fixed.
Hub gears were around then but were so heavy you wouldn’t race with them.
The derailleur bicycle gear was invented first with 3 or 4 gears, now on a road bike it will be 20 or 30 gears and on mountain bikes its 27 and soon to be 30 with the use of a double or triple chain ring at the front and on the back wheel 9 or 10 sprockets.
Campagnolo and Shimano make nearly all the gear shifters, front derailleur, rear derailleur, chains and freewheel sprockets for road and mountain bikes, from reasonably priced to very expensive.
The main difference is the use of steel, alloy, titanium and carbon, steel for the cheaper gears and carbon and titanium for the top end equipment and so it weighs less.
There are other makes of gears and shifters, for example Grip Shift, Sachs and chains are made by a few other companies, but the big two are what you see on 99% of bikes.
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