Just to keep it simple, there is exactly one definition of espresso: coffee produced by forcing hot water through coffee grounds at very high pressure, typically 9 atmospheres.
There's a bit of wiggle room with the pressure, but if it's much lower than that it's not espresso. For example, a "moka pot" aka "stovetop espresso maker" can make good coffee, but it's not espresso. These contraptions produce about 1.5 atmospheres of pressure. The result doesn't resemble the flavor or viscosity of the real thing. The pressure requirement isn't arbitrary; a major part of what characterizes espresso is that the high pressure emulsifies the oils from the coffee bean. This creates the syrupy mouthfeel.
Other factors that have been mentioned—grind size, water temperature, etc.—are incidental to the process. You need a fine grind size to make the process work, and uniform grind to make it work well, but the pressure is what makes it espresso. The correct water temperature (which can vary from 196°F to 205°F) is important for dialing in the right flavor, but this is no different from other coffee processes, in principle.
There is absolutely no correlation between roast and espresso. The idea of an "espresso roast" is a con. It was a way of convincing people they could simulate the taste of real espresso by brewing coffee with burnt beans. Most 3rd wave coffee roasters don't even go anywhere near the 2nd crack in the roasting process, because they want you to be able to taste the beans. Even traditionalists in Italy ... their dark-roasted espresso is usually what we'd call a "city" or "full city" roast in the US (medium roasts). Nowhere near black and oily. If you want to taste the full flavor and origin character of the coffee, you need a light or medium-light roast.
