It's all coffee, after all
If you order a black coffee and are handed a shot of espresso, you'd probably be pretty disappointed—and vice versa. That's because a cup of drip coffee is very different than a shot of espresso. But what makes brewed coffee different from espresso, exactly? They're both coffee, after all, and technically, both coffee and espresso can be made from the same coffee beans. The difference between coffee and espresso has to do with the method of preparation, starting with the beans themselves. Coffee beans designated for espresso are generally roasted for a longer amount of time than beans meant for drip coffee. Espresso beans are also ground on the finer side, more like sand than gravel.
While the type of beans you use is important when it comes to taste, the main difference between espresso and coffee has to do with the way the coffee is prepared. Technically, you could use espresso-roasted beans to make drip coffee and dark roasted coffee beans to make espresso if you ground the beans correctly and used the right gear.
So, what's the right gear to make espresso? It sounds obvious and kind of dumb, but you need an espresso machine. That's because espresso, by definition, is a strong black coffee, made by forcing hot water through tightly packed grounds. That extraction process is what gives a shot of espresso its signature layers: a shot of coffee at the bottom with a small layer of foam, or crema, at the top.
If you're making drip coffee, you've got a few options for brewing. Since the grounds are mixing with water for a longer amount of time, the grind can be coarser than that of espresso. To make the coffee, you can use the pour-over or drip method of brewing, or the immersion route, like with a French press. Either way, the coffee you get from these methods will generally have a milder flavor than a shot of espresso, and there won't be any crema.
So the difference between espresso and brewed coffee has everything to do with the way its made. These methods of preparation are what dictates the flavor more so than the beans—though using the right style of beans can make the difference between an OK cup and something extraordinary.