Answer: You are asking a very interesting question. Whether or not a plant would be considered invasive does depend on where you live and how you wish to define invasive and in some cases whether or not it has been classified as such by the government. (Some plants though such as purple loosestrife seem universally considered threatening and are no longer legally sold in many states.) In some states there are very strict definitions and lists of invasive plants or plants of concern, sometimes even taking into account different areas within the state, in other states less so. It can also depend somewhat if you are living on the edge of a rural area where the plants could easily spread unchecked, or in the center of the city where most yards are very controlled. Too, it depends on details such as which type of Euonymus you are thinking of. Euonymus alatus (burning bush) is apparently now considered invasive in some areas but others such as Euonymus fortunei cultivars are not. And you will find that many potentially invasive plants are widely offered for sale and have been widely planted.
Here for example is just one description of the burning bush issue.
English ivy or Hedera helix is certainly seen as a big problem in the Pacific Northwest where it is invading natural areas. On the east coast it is more recently being identified as a problem or potential problem in some areas. Here is a sample listing for it, including information about some of the states' responses to it.
As you can tell, this is quite a subject of debate. Over time we seem to be identifying additional plants of concern. If you have a doubt about using a specific plant in your local area I would suggest you consult with your local county extension to see if it seems to be a potential problem locally, or not. I hope this helps.
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