We sometimes call serendipitous ones volunteers, the undesirable are interlopers or weeds. I am excluding the semi-infinite number of weeds in lawns. I have a friend whose large lawn, while a continuous swath of green, even has some grasses in it. He is totally unconcerned as to what gives it its color. Whatever is low and slow growing is welcome.
Weeds are obviously in the mind of the beholder.
When my middle son Jim was in high school he became enamored with wild Geraniums growing in the nearby park. He scattered their seeds around the house near the foundation. For the next decade I was pulling out the plants. To me they were weeds. He might have taken his cue from his sister Ann.