When plants come up in the garden where we don't expect them, we might call them "weeds," or "volunteers," or "naturalized."
I didn't plant these "volunteer" snapdragons. They just keep reseeding themselves, starting from a lone plant that was there when I moved in. They choose their colors themselves.
The irises in the back have spread over ("naturalized") from a much smaller clump.
The mullein (Verbascum thapsus) really is a "weed," but look at how awesomely large it is! A biennial, this is its second year, and it will put up a 12-foot flower stalk. It looks positively prehistoric. I leave a couple in place because I like their looks and their spread is fairly easy to control.
Unlike the lamb's ear (Stachys byzantina), which comes up everywhere. I laugh at myself for oh-so-carefully transplanting a clump the first year, and worrying about its survival. Now I rip it out wholesale when it's in the way. I've given away pots of it to friends with kids who adore petting the fuzzy leaves. But I still have a lot of it. The silver foliage is pretty and the bees (both wool carders and honeys) really love it.
Actually, a lot of my gardening seems to follow the natural spreading habit of plants. I'll find a plant coming up in a new spot and think, "OK, I can go with that," and next thing you know, I've got a new flowerbed.