Not exactly the same. The design was finalized by Charles Thomson in 1782 and made into a die at that time, with the impression looking like this: https://en.wikipedia.org/wiki/Great_Seal_of_the_United_States#/media/File:Great_Seal_of_the_United_States,_c.1782-National_Museum_of_American_History-_DSC05352.jpg

Each seal varies in design but has the same elements. Similarly, the President's coat of arms is defined by list of elements, not graphic design per se, and most recently was defined by EO 10860: https://www.archives.gov/federal-register/codification/executive-order/10860.html

The coat of arms elements are the same as those of the seal, plus a ring of (now 50) stars. The constellation of 13 stars and the rays and clouds are allowed to vary, for instance. Feathers aren't specified but 17 on each side goes back to at least FDR (check your one-dollar bills). That means that it is similar enough to Washington's symbol to qualify, but also is pretty much the same as every president (or occupant) has used.

Trump seems to be laying a continued claim to the presidential seal in the public eye, but it may be that the cut ribbon in closeups of his seal (visible on 45office.com which otherwise appears to be a placeholder website) is enough to prevent it from being an illegal personal use of the American seal criminalized by 18 USC 713. It may even be that the three stars represent three state governors that have already agreed with his continuing Trump administration tactic.

https://en.wikipedia.org/wiki/National_Security_Act_of_1947?oldid=cur 14 stars +3 more =17 for Trump :-)

Probably three branches of government.