I think both have value. I like & would aspire to (but likely never attain) the worshipful company's definition.
I once asked Bob Oakes, the first smith I learned from, what it took to be a master smith. His answer; 'I suppose you'd call me a master smith, since this is my forge & I run it.' He wasn't being ego-centric by the way.
What he meant was that as the owner of his company; which employs him, his son, a variable(?) number of smiths & allied trades, an apprentice (and boy can that kid smith!) and various younger smiths either gaining work experience or teaching specific courses on his behalf, he was the other definition of a master smith. So that meaning of the term 'Master' clearly has credibility.
Note as I said that he sometimes has 'beginner' or 'junior / journeyman' smiths on work experience - this is one of the ways I'd pesonally judge any master tradesman - they're sufficiently comfortable in their own abilities, skills and business that they are willing to give new talent a 'hand up'.
I doubt that Bob is alone in this, and I suggest another definition of master smith: Smiths who are willing to give budding smiths meaningful work and the credit for it, are masters in the martial arts aka Yoda style.