Which gas makes bread rise?

Carbon dioxide, produced by yeast eating the sugars in the dough. The gluten network formed by kneading is elastic enough to trap the bubbles rather than letting them escape, which is why bread has a crumb and why flour with little gluten makes a dense loaf.

Yeast is a fungus, and it produces alcohol alongside the gas - the same organism and the same reaction as brewing. Most of the alcohol boils off in the oven, and the flavour compounds it leaves behind are a large part of why bread tastes of anything. A long slow rise makes better bread mainly because it gives those by-products time to accumulate.

Sourdough does it with a partnership rather than a packet. A starter is a stable community of wild yeasts and lactic acid bacteria that keeps out competitors by making the dough too acidic for them; the yeast supplies the lift and the bacteria supply the sourness. Baking soda works differently again - a chemical reaction with an acid that releases gas immediately, which is why soda bread is mixed quickly and baked at once.