The same. In this context, there is no difference. Погнали- slang.

In fact, I don't get it either because the word "Пошли" is the past tense form of the word "Идти" ‒  они пошли в театр (they went to the theater), for instance. So, literally it's the same as if you'd say "Let's went!" instead of "Let's go!" in English lol. But for some reason we say it that way, but only in the case of the expression "Пошли!" To me the expressions "Пойдём!" and "Пошли!" don't defer in terms of style and they are used interchangeably in daily life. In books you are probably more likely to see "Пойдём!" used. Speaking about "Погнали!", this word sounds like a slang to me. It means the same thing. Personally, I use it a lot and everywhere. This word sounds fine, but still it is a slang. You can easily use it in the company of friends. If you are going to go somewhere by a car, you can say "Погнали!" or "Поехали!", but neither "Пошли!" nor "Пойдём!"

одно и тоже

In a different context, these words mean similar but not the same thing. For example, if a call or request, consisting of one word, "Come" - colloquial and not a correct expression, but very common. All people understand it. "Come" - absolutely correct and clear turn. That's what they say educated people, it is - the norm of the Russian language. It is a beautiful turn. "Chase" - jargon, so say those who stand out from the crowd of a few vulgar words to show their independence and otherness. There are many people among students and youth. This innocuous verbal conduct, but we can not say among respectable people, they will be surprised because that failure to comply with decency. Maybe they will laugh if it suddenly tell a foreigner. In general, the need for a proper understanding of the context :) I apologize for any errors in English.

Существуют разные способы формирования повелительного наклонения глаголов. Подробно здесь: http://www.bibliotekar.ru/russkiy-yazik-2/172.htm