It is different in that those medications are probably FDA-approved. The vaccines are not FDA-approved. But that may not be what they mean by saying it's different.
I mean, they all have Emergency Use Authorization from the FDA. I think the difference between that and full FDA approval is more about formalities than anything else. And I doubt anyone refusing to take it for lack of FDA approval is basing it on the differences between what it takes to get an Emergency Use Authorization and full approval from the FDA.
Beyond that, lots of stuff that gets FDA approval ends of having unexpected side effects too.