Trump and the 2nd amendment

If a politician says they want to expand criminal background checks for gun purchases, they will typically be fiercely opposed by the NRA and a strong segment of voters, who will accuse that person of wanting to "take our guns".

But... the NRA supports Trump, and Trump said the following about his version of stop-and-frisk which he wants to implement nation-wide:

"if (the police) see a person possibly with a gun or they think may have a gun, they will see the person and they’ll look and they’ll take the gun away"

Did he just misspeak? No, because not long after that, at the first debate, he re-iterated this. Why is this OK with the NRA and like-minded people, but expanded background checks are not? How would such a policy work with open carry laws?

One thing to note is that, when Trump says something like this, in the context of the conversation he is talking about black and Mexican people. Is that what makes it OK? Sometimes people try too hard to make things like this about race, but I honestly can't see what other difference there is. What am I missing?