I wear a slightly different wardrobe when traveling than I would at home. (I'm American.) For example, I wear sturdy shoes for lots of walking (tennis shoes/trainers, Merrell brand, or my Teva brand sandals) because otherwise my feet hurt incredibly, and I'm carrying a larger purse or bag than usual (to carry small water bottle, granola bar, etc). And I'm often trying to dress for a whole day out in changing temperatures. So yeah, I often look a little...touristy.
Basically my mix-and-match travel wardrobe may look a little odd, but when I dress for work here at home it's much smarter, more tailored, etc. So I think part of it isn't so much where you're from, but what you're doing there - i.e. living day-to-day or visiting.
I think that you might have triggered a possible solution in my brain.
I find that a lot of Americans view travel as an 'activity'. So they will prepare for a day out, carrying a large bag with drinks, snacks, and other things. They'll dress in specific outfits that they wouldn't usually wear on the street (hats, running shoes, rain jackets when it's not raining, etc.)
Perhaps because there is far less of a 'drive everywhere' culture in Europe, I (and most people I know) don't view travel the same way. A day out walking around is just a normal Saturday, and doesn't need specific preparation. Of course, clothes should be weather-appropriate, but they'll be something from my everyday wardrobe. Ditto shoes. I might carry a slightly larger handbag, if I need to carry sunscreen, but that's about it.