What's the difference
So, let's talk about the difference. Difference between where you go, what you think you will get, and what you do get. The problem with un bistro, un brasserie, and un bouillon is that these three are often confused.
La Bistro
The invention of this name, as various sources suggest, comes from the early 19th century when the Russian army was in Paris: as they ordered their food and drinks, they would shout in Russian “faster”, which is almost the same “bistro”. Even today, the main thing is that the food is served quickly, and traditionally the menu often written on the board behind the bar. The place is as local as local can be - warm, cozy, in everyone's quartier, simple, and classic. Le bistro is where you eat with no fuss or just order a cup of coffee and usually sit reading your book or chatting with a friend, using that one cup of coffee as a justification to spend much more time than they would expect or love.
La Brasserie
A very different story surrounds la brasserie, which is usually grander in its appearance, bearing a more Art Deco style. Once you have visited more than one, you will notice their significant difference from other establishments. They seem posher and stiff, yet they are from being restaurants. The food is simple, yet more elaborate than at the bistro. The service can last all day long (but not always, especially at very good brasseries), offering several meals a day. Steak is almost always served, as are fries, seafood, and classics like iles flottantes or profiteroles. This will not be a place in which the menu changes daily or even monthly as the brasserie is about the classics that we love. Yet, recent years have changed the scene a bit, and next to those classics, new ones are born, serving local, seasonal, and more elaborate versions of our very much-loved classics.
Le Bouillon
Some sources say that it was in 1855 when Baptiste-Adolphe Duval opened the first bouillon, but others say that it was butcher Pierre-Louis Duval who did so in 1860. No matter which is the true story, one of them did rise to an establishment serving broth and later the numbers grew to over 200 during the Belle Epoque. Over the next decades, more than just broth was served. It was a cheap place allowing its diners to order classics like eggs mayonnaise (oeufs mayonnaise), poulet frites (chicken with fries), tête de veau (veal), salads, poireaux vinaigrette (leeks with vinaigrette), and so on. Products purchased and cooked in large quantities allowed the prices to be low. This might not be a fancy way of dining, but it most certainly is very traditional and local.