A cultivated plant that escapes from cultivation is known as an escaped cultivar in plant books if it is a species known to do this in a certain area. Sometimes this becomes an invasive plant, and although feral, we mark it wild on this site. An escaped cultivar that doesn’t survive more than a few generations, and is limited to a very small area, and doesn’t spread is known as a waif. A waif happens here and there, but is too uncommon to mention in a Flora (plant list, or book). An escaped cultivar species that becomes naturalized or invasive in an area of significance, and remains feral forever, will be added to a region’s Flora.
For this site, we leave it marked wild, unless you planted, or transplanted it, and now you are watering it, pulling the weeds, and have it in a yard. Then it would be captive or cultivated.
The designation of cultivated is not perfect, but it is basically to say that the species was not found in the wild, but it was obviously planted and is being cared for.
So, if you are looking at landscaping, experience with plants would come into play. You could determine that some or all were planted, and are being cared for, but then notice a weed, and the weed would be considered wild. It is wild because even though it was once a plant from another part of the world or country originally (wild some other place) or grown in a garden originally, this species now spreads on its own, and will continue to do so “forever.”
On the other hand, if you are in a wilderness, and you see a plant that is non-native, this is still wild, despite the fact that its ancestors were maybe either a cultivated plant, or simply from another part of the world.
It is important to document non-native plants when they escape into open spaces, or into wilderness, or even into urban fields and lots. Invasive plants are a big problem and the focus of many projects to remove them from wild areas.
A waif is not considered to be something that could be in danger of becoming invasive.