A green card allows you to live in the US, but you aren't a citizen. You wo'nt be able to vote, and if you leave the country for a certain amount of time you would have to re-apply for your green card again. Once you have lived in the US for a certain amount of time you can apply for citizenship, once you do this you are like any other US citizen, you can vote and you can leave the country for as long as you want and still be allowed back in.