No matter what, every alcoholic beverage you drink contains the same type of alcohol. It's called ethyl alcohol, also known as ethanol, and it's pretty much the only one that won't immediately kill you (please don't try drinking isopropyl alcohol). Despite this fact, various beverages do have a few differences: Liquor has a higher concentration of ethanol that wine does, and wine has a higher concentration than beer. This is why whiskey is served an ounce at a time and lager is served by the pint. There's also the fact that certain spirits are served with certain mixers. Mix rum with Coke or vodka with Red Bull and you'll feel very differently than if you had mixed gin with a caffeine-free beverage like tonic water.
One possible way that different types of alcoholic drinks really can give you a different drunk—that is, one not shaped by your expectations—is through something called congeners. These are byproducts of the fermentation and/or distillation process, and they can vary a lot among alcoholic beverages. They mostly explain why tequila is a different color than whiskey and why gin tastes different than vodka, but it's possible that they can also affect the way you feel after drinking. There isn't enough research either way to know for certain, so the jury on how congeners affect your buzz is still out.
But the most likely explanation for why you feel different after different drinks? You expect to. Studies have shown that our expectations have a big effect on how we feel after drinking. According to an article published in Alcoholism Clinical & Experimental Research, even when every participant in a study drinks until they have the same blood-alcohol level, they show different levels of impairment. Research suggests that the way they act depends on the way they expect to act: those who expect not to feel drunk actually feel less drunk. Likewise, other studies have shown that people also feel less drunk in situations where it's a good idea to act like you're sober. That means the fact you couldn't stop dancing on tequila shots at your cousin's wedding really does mean you'll probably want to dance the next time you have tequila, but it's not the tequila's fault. It's because you expect to get dance fever again. Learn more about the effects of alcohol in the videos below.