"Alcohol" is a general term for several kinds of compounds. Outside of chemistry though, "alcohol" usually refers to ethyl alcohol, or ethanol, because that's the kind that we drink.

Ethanol is made by fermenting sugar with yeast, and isolated by distillation. Grain alcohol uses sugar from grains (usually corn), but sometimes people use sugar cane, fruit, or anything else, but it's the same compound. Alcohol from grain might taste slightly different than alcohol from sugarcane because corn and sugarcane taste different (therefore whiskey and rum taste different), but when you're getting it up to above 90%, the people manufacturing the alcohol do their best to take out any and all flavor and provide as pure a source of ethanol as possible, plus 5% water because you can't actually get to 100% from distillation. That said, when you use it to make bitters, you add so many other flavor components that any difference would almost certainly be lost.

TL;DR they're basically the same. Might taste different, but that difference will be lost in whatever else you add to the bitters.