I'm tending to my scented Geraniums when I think about how they're not Geraniums at all--they're Pelargoniums. Due to centuries of mistakes (dating to the 1700s!) we still call them Geraniums. This is an example of a plant being called a name of a separate genus which still exists (there are "real" Geraniums).

But Coleus is another plant that I grow every year, and that genus (Coleus) does not exist anymore, as far as I can tell (correct?). Every plant I see called "Coleus" is either Plectranthus or Solenostemon. But we all still call them Coleus.

I'm guessing there are a ton of examples, but by their nature common names are so common that we probably don't even realize it (I don't, at least). And when the common names are a current or former genus name to a similar or related plant, is it any wonder people get confused?

Using correct and updated botanical names is very important for botanists and other scientists because the updates reflect more recent findings and understandings as to how various species are related to one another. Scientific knowledge is ever-changing as understandings expand.

For us laypeople, using common or traditional plant names is perfectly okay most of the time. The purpose of naming is so we have a common understanding of the plant being referred to. If you use Coleus here, most everyone will not exactly what you are referring to, although perhaps not the specific variety or hybrid. I agree that trying to be scientifically correct at all times on a site like this is not always the best thing. If you post a photo of a plant then we can all see what it is, regardless of what anyone calls it.

One other note: Common names are sometimes very regional or applied to more than one species and that can lead to confusion that botanical names avoid.

Yep. I think the unique issue we have as gardeners is when the common name and Latin name are identical and known around the world for decades or centuries, then the Latin name changes.

Amaryllis are another example I just thought of. What the whole world knows as Amaryllis are not in the genus Amaryllis.

Well as there are so many people whose first language is Latin, it can be very confusing.