Al-Qaeda and ISIS do not have the same goals. To put the difference very roughly, ISIS has 100% religious goals, but Al-Qaeda's goals are pretty much basic "freedom fighter" stuff.
ISIS as an organization has two goals. To set up a Caliphate and to bring out about the End of Days. (Those are two somewhat separate things, and not every member of ISIS wants both things.) What's important here is that both are extremely vague goals. In short, ISIS does not actually have much of a plan.
Al-Qaeda on the other hand essentially wants to drive out the US military (and any other "occupying force") from the Islamic lands and to overthrow all the dictatorial rulers backed by the United States and their allies. (This includes the destruction of the state of Israel, which they see as illegitimate.) While Al-Qaeda is also deeply interconnected with the same ultra-conservative branch of (pseudo-)Sunni Islam called Wahhabism, they are on average a lot less crazy and nonsensical bunch than ISIS.
(From what I've gathered, Al-Qaeda is actually lot less fanatic than it used to be after the birth of ISIS, as most of the worst bunch left Al-Qaeda for ISIS.)
The main difference I guess could most easily be summed up in the fact that you can totally negotiate with Al-Qaeda and reach agreements that both sides could accept. ISIS you can't work with. (In large part because you can't make deals with an organization that has only a vague idea what it wants.)
This is why in practice US and other Western nations have recently worked quite a lot with Al-Qaeda to fight ISIS. (Mostly indirectly but still.) Al-Qaeda and the US might be sworn enemies, but both see the difference between a mortal enemy and a doomsday cult.
Also it's important to understand that when the Western media says "ISIS fighter" or "Al-Qaeda affiliate", those are extremely generalized concepts that often do not mean what you'd think it means.
Many of the groups fighting for ISIS are not strictly speaking ISIS, just local armed groups that ISIS is paying to fight for them. These are also groups you can negotiate with. You can also generally relatively safely disarm them and just send them on their way, because they're not generally fanatics. (This is starting to be important now that ISIS has started to lose the war.)
"Al-Qaeda affiliate" (a term often used but rarely explained) is an even more vague concept. These affiliations can sometimes come and go, and the variation is even greater than with ISIS. In Al-Qaeda you have everything from your stereotypical bloodlusty fanatics and "true believers in the cause" to groups that are pretty much just local armed militias mostly interested in protecting "their own", to groups that simply have political goals that are closely enough aligned with those of Al-Qaeda that they can work together. (This is a problem for the West, because telling the different groups apart is not easy for an outsider, and a simple change in leadership might change a group away from fanatic Islamism, or towards it.)
As for Nazis and religioun, that's a really complicated story, but you most certainly can't simply call them "religious". (Especially not Christian).
It's actually pretty interesting stuff. I recommend reading
the Wikipedia page.