You’re running a system’s setting with a different system and calling it “the same system”.
But I'm not.
At absolutely no point did I say it was the same system. At absolutely no point did I say "I'm running the Shadowrun system." My exact words were "I run Shadowrun." You added "system" entirely in your own head.
Yes, obviously, if I was advertising a public game at an LGS, I would state up front that I'm not intending to use the Shadowrun system. I wouldn't want people to be caught off guard by that. And even when I run these games privately, I still tell people ahead of time that I won't be using any of the stock mechanics. Even for players who've never played Shadowrun, I still put that information out there so that they don't wander into another Shadowrun game expecting the same experience.
But the thing you objected to was me saying "I run Shadowrun." And you immediately assumed I included the word "system" and launched your entire objection on the basis of that.
And this is where I think we have fundamentally different philosophies about what roleplaying is, as a hobby. Because when I say "Shadowrun" I mean a fascinating world of alt-history near future cyberpunk mixed with Tolkien-esque fantasy that really shouldn't work, but somehow manages to actually use the disparate elements to reinforce one another, turning magic and monsters into new layers on cyberpunk's existing themes.
And when you say "Shadowrun" you apparently mean "One or more entries in a very specific list of different d6 dice-pool based systems".
Yes, obviously if someone said they're running D&D and then it turned out they were running Dungeon World, I'd be kind of perplexed. But that's because D&D itself isn't a setting, it's a system. On the other hand, if someone said they were running Eberron, and then it turned out they were running it in the Gumshoe system, I'd be fucking psyched. That would be such an awesome way to explore that particular world. Imagine how cool it would be take the 1920s vibes and shades of cosmic horror and turn them into an investigative mystery story, without all the combat heavy D&D mechanics getting in the way.
In the case of Shadowrun, yes, it is both a world and a system. But of those two things, the world is far more important. The system only exists as a framework through which to explore that world. Shadowrun as a world can exist in any system (that doesn't mean it will feel the same in any system, but it can exist), as evidenced by the fact that its official systems have taken so many different forms over the years. But the Shadowrun system without the Shadowrun world is nothing. It's meaningless. A useless appendage lacking the story that gives it form.
This is not to say that changing the system will not change the world in certain ways. Systems shape the rules of a world. They are instrumental in defining many elements of tone and genre. But lots of things change the feel of a world, first among them being the GM. Even if you and I both run Shadowrun using the same edition, with scrupulous attention to exact implementation of the rules as written, we won't be running the same Shadowrun. We're each going to have our own ideas about how that world operates, about what is and isn't possible, or normal. We're going to describe characters in different ways, play out interactions in different ways, put emphasis on different things. There is no pure, unadulterated version of a setting in roleplaying. So why get so hung up about adherence to specifics of the mechanics, when everything else is already up for grabs?