Yes, there are certainly differences in what you get dependent on the speed at which you let your dough rise. I am talking about first rise here; the second rise is generally the same length for mid- and long-fermented breads, and people who proof quickly usually don't bother with a second rise.
Quick rise: 40-60 min, 25-35°C
You get a very vigorous yeast colony that rises quickly. It suffers from overcrowding and produces characteristically smelling compounds, including thiosulfates and some ammonia.
This quick process is mostly used by home bakers. Typical reasons to choose it are:
- you're pressed for time,
- you love a bread that smells "yeasty",
- you're uncertain of your skills or your yeast quality and decide to use more yeast and/or higher temperature, to be sure your bread won't be a dud
- you don't know that there are slower options, or that slower options produce different results, or you don't care enough about the taste difference to bother with
The time is normally sufficient to hydrate the dough well, but you don't get any noticeable autolyse. Any gluten development has to be achieved mechanically. For good results, you have to make sure that you don't over- or underknead. You may have trouble shaping this into products that require good gluten development, such as round pizza bases or braided breads.
Standard rise: 2-5 hours, 15-20°C
This creates the most neutrally-tasting bread. You get a steady, nice fermentation without noticeable byproducts, and interrupt the colony's development while still very young. It produces a good texture, and you have a bit more leeway with kneading.
Retarded fermentation: 1-3 nights, 4-8°C
This technique has been gaining popularity in the 21st century, and is frequently considered "artisanal" bread. The long fermentation lets you develop a bit of the taste that has been classically produced by using sourdough, mostly based on acetic and lactic acid. You don't get the full-blown sourdough taste, but it's reminiscent, and the aroma is more complex than either the standard or the quick rise.
You can either knead the dough, or go completely for autolyse. Also, the texture is quite different from the shorter rises. The dough itself is very well hydrated, but becomes to some degree plastic rather than elastic, and this is noticeable also in the baked bread.
Reasons to choose this technique are:
- you want a sourdough-like taste without bothering to do the whole sourdough process
- you enjoy the idea of making modern artisanal bread
- you prefer the texture produced by this method
- your logistics prevent you from doing everything on the same day
- your logistics require you to minimize your hands-on time spent baking, so you want a no-knead (and possibly one-pan) recipe.
The above is a very rough guide. The ranges don't overlap on purpose, because I wanted to point out the most typical way of doing it; in reality, you have a continuum. If you proof your recipe such that it rises in 1.5 hours, you get dough/bread that's midway between the typical classic and quick rise.
The result descriptions aren't precise, they're rather broad guidelines. Especially the texture will depend a lot on the recipe ingredients and ratios, and your kneading technique.