Hm. OK, I'd like to come in defense of Lawrence (not that he needs one, mind you) here, because maybe there's a problem with language. I'm sure things get different names in different countries (for example the different kinds of sugar in England and America). So here it is.
In America there are two main kinds of leaveners -- baking powder (which is used to make cakes and quick breads like Irish Soda Bread), also known as chemical leavener and, very possibly in some countries, instant leavener. Baking powder is a combination of acid powders and base powders that react to produce carbon dioxide when exposed to water and, the newer kinds (as in, some 100 years ago or so), double-acting baking powders also produce another dose of carbon dioxide when exposed to heat.
We also have biological leaveners, usually called yeast. You can get several different kinds of yeast in America -- sourdough starter is sold in many places including by mail order, and once activated is a living thing you have to keep properly or it will die.
The other three kinds are basically exactly the same organism (brewer's yeast) packaged in different forms.
You can get yeast cubes which are often seen at the refrigerated section in the supermarket -- these are basically living yeast packaged with an awful lot of other dead yeast cells, they are not very active and if you don't use them very soon after buying they can die completely; old recipes were written with these in mind and that's why there are lots of risings and lots of time.
You can get powdered yeast (also called Active Yeast). These are yeast cells that have been carefully dried, so they get dormant and you need to reactivate them by rehydrating the powder. The drying process basically kills the external cells in the tiny blobs. You use way less active yeast powder (by weight) than the old cubes. Since not all cells are live, the recipe tends to take about the same time and number of risings for old yeast cubes. If you did use the same weight of active yeast I'm sure you'd have a Lucy Ricardo moment and have bread taking over your kitchen.
And you can get Instant Yeast, also known as Bread-Machine Yeast. This is exactly the same creature (brewer's yeast) you get from the cubes or the active yeast powder. The biggest difference is that this yeast is dried by a different process that takes almost all cells from active to dormant very quickly, so way fewer of them die in the process. If you only have instant yeast and want to replicate a recipe for active yeast, use 30% less and you have converted the recipe successfully. If you are used to active yeast and want to convert to instant yeast, use 2.25 teaspoons of instant yeast for each packet of active yeast in the recipe (I forget if it's 7 or 9 grams of instant yeast).
The thing with instant yeast is that you don't need to proof it. In fact, if you do, you'll need to follow the same number of risings and timing as for the other two kinds.
But the cool thing is, if you mix the instant yeast with the flour and use water in the proper temperatures (from 105-120F), then you can knead the dough, give it 10 minutes in place of the first rising, shape the dough, do the second rising and bake it. That, right there, cuts at least one hour in the rising time. The end product is identical to the traditional risings.
If you do what I do (I do the second rising in the microwave, it takes from 6-15 minutes), and you are fairly well organized, you can have bread coming out of the oven in 60-90 minutes from start to finish. If you are fairly disorganized, you can have bread in just two hours. Which is less than it takes to rise it by the traditional methods. That's why some bread machines get bread so fast.
Now I can hear what y'all are thinking. That's bound to be bad bread, just like machine bread. I will laugh at you. I'll be the very first to admit that this is not the way to produce sourdough bread, because the very flavor of sourdough comes from getting sour and there isn't enough time to sour in 60 minutes without cheating like using beer and/or vinegar etc. But if you are making anything like sandwich breads, which are not as assertive to begin with, or stuff with a more delicate flavor, like challahs etc, the instant yeast method runs circles around the traditional methods, because all the flavor of the ingredients just pop in your mouth to the point you can tell if you used a good flour like King Arthur or just an ordinary flour and you can even tell if the flour was rancid or not, which many breads made with the traditional methods hide very well.
In fact, I have had plenty of chefs tell me to my face that "unless you let the dough rise slowly, the bread won't have any flavor" and then say they loved my bread and ask for the recipe. Once I had a chef talk to me at a party spouting exactly those ideas and it was all I could do to not tell her that if that was true she should not have eaten half a loaf of the bread I had just baked and brought to the party. Just to give you some food for the thought, there would be no good breads in warm places like Portugal, Spain, France and Italy if the only good breads came from rising slowly at 40-60F. Bread just rises faster in places like that, you wait until the dough about doubles in size and you're done, if you want sourdough bread you use sourdough starter which will have the right blend of yeast and bacteria to produce the right flavors. As long as the flavor is good, why should anyone care how long it took? Are we at the point that the end product doesn't matter, what matters is how long you slaved over it? Because usually, as the recipient of a letter, for example, one doesn't care if it took one person 3 hours to type a letter that other people can type in just 5 minutes, we care the letter is done (unless you are the boss and you don't want to wait for that much inefficiency).
As for pizza, I'm here to tell you that my entire family came from Italy, some from the North, some from the South. Every single great-grandparent thought pizza was different than what the others thought. It is quite clear to me, looking at the recipes, that pizza in their families was either the same recipe as their bread or extremely close to it, so of course, given the number of different breads there are, the pizzas will be different too. But rest assured it's pizza and bread anyway, there's no good reason to think one is more Italian or more genuine than any other, they all taste good. It's only in the last 50 years or so that "recipes" for pizza became more standardized. Also, keep in mind that workflows in restaurant are vastly different than at home and many times recipes for home will totally fail in a restaurant and vice-versa. For example, few people have ovens that reach 500-600F consistently, so of course a pizza recipe for a home oven will be very different and cook with a different timing at 400F than whatever the pizzaiollo is using -- the flour is different, the hydration (ratio of water to flour) is different, temperature, timing etc.
Just to give you an idea of how different people see it totally differently, my mom's dad, who came from Piedmont (sp?) would send any pizza from a pizzeria back. Why, you may ask? Ironically for the same reason they are burnt in the first place. His generation, who was forced to use wood ovens, would think that only a completely careless person would not pay attention and let them burn. My mom and her siblings say he had never been happier than when the first pizza came out of the newly bought gas oven, crispy, perfectly golden brown and with not a trace of char anywhere. Meanwhile, we people who grew up with thermostatically controlled gas and electric ovens would never go to a restaurant and get a pizza that anyone could produce at home by just dialing 400F and the appropriate time at the timer and just come back to perfect pizza, no no no. We go to the restaurant and they are forced to get a wood oven to make "authentic" pizza for us and they have to keep looking at it or it will be un-edible -- with time, pizzas started coming out of the oven increasingly more charred, just to prove it was made the "traditional, authentic" way with a wood oven. It's got to the point that I avoid certain places because the pizza is now bitter and yucky. It's in fact the same crap that happened to pasta -- 50 years ago pasta was cooked to death here and someone told people pasta should be "al dente" so people started cooking pasta less and less, so now there are people and restaurant serving practically raw pasta, yuck. I hope that fad disappears soon.