I see there are two different Wikipedia pages for strain wave gearing and Harmonic drive. To my knowledge they are the same. Harmonic Drive is the trademarked name of strain wave gearing by United Shoe Machinery Corp. Am I doing any mistakes here or what?
To quote the opening line of your linked wikipedia article
"A harmonic gear is a strain wave gear"...
The first line is quite explicit in saying that they are the same thing. The second line says:
Harmonic Drive is trademarked by the Harmonic Drive company.
I don't really see any reason to assume they are not the same thing. "Harmonic Drive" is the brand name.