The first amendment doesn't protect using someone else's brand with only a few exceptions, parody being one, satire not being one. As for the difference, parody:satire::sarcasm:facetious
Among other things, it suggests that the dichotomy of satire and parody is artificial, and furthermore should not be within the realm of the courts to distinguish.
Excellent paper. For those who don't want to download the PDF, the relevant paragraph is as follows:
"The dichotomy approach is certainly easier to apply: if the new work arguably criticized or commented on the original, a parodic character reasonably can be perceived ... and a fair use finding is quick to follow. On the other hand, if the new work used the original work as a mere vehicle to criticize something else (such as society in general), it is satire, not parody, and therefore not fair use. However, while the parody/satire distinction has become the central issue in many cases, the proper dividing line between quintessential parody and satire is blurry at best. Creative
lawyers and judges have taken advantage of this blurriness..."