It's a bit different.

First, Reagan only referred to Springsteen as a hopeful songwriter in a speech on the campaign trail, and that was about it, since Springsteen didn't authorize use of the song on the trail. It should also be noted that the incident came in the context of a presidential campaign ('84) in which Reagan likely would've gotten reelected doing anything short of using the Soviet national anthem in his ads. Second, "Born in the USA" wasn't critical of Reagan (or Reagan-like figures) specifically.

Meanwhile, Trump used the song without asking (of course) and received a cease-and-desist, in the context of a very close election campaign, and as a "Fortunate Son" that dodged the draft for the exact war the song was written about.