The only difference is the sparkle effect that happens when the Pokemon enters battle. The shiny coloration is exactly the same.
Star sparkles (left) vs square sparkles (right):
Shinies found through Masuda Method have a 15/16 chance of having star sparkles and 1/16 chance of square sparkles. Shines found through wild encounters are the opposite, with a 1/16 chance for stars and 15/16 chance for squares. All shinies from Dynamax Adventures are star shinies.
Some people will refer to square shinies as "ultra shinies," but this is misleading. This is because when news on shinies in SwSh was first getting out, it was falsely reported that square sparkles had a blanket 1/16 odds, before it was corrected that those odds only applied to Masuda Method. You might see people still make this mistake, especially if they aren't an active shiny hunter.