No.
Derivative works need to be licensed unless the derivative work is a parody or commercially worthless commentary on the original work.
So the rules are the same for everyone (n.b. they are in the same locale).
But if you derive a work from Coca-cola's logo ... and you are a soft drink manufacturer trying to mimic them for gain, you are going to be pilloried in court.
If you derive your work from Coca-cola's logo and you are making fun of the product or the logo or the company, whether you manufacture soda or not... it is legal to do so under fair use. (No competitor in their right mind would attempt it due to court battles, but they should theoretically win.)