Vegetable oils are likely called vegetable oil because of the thought that "vegetables are good for you". It's all about packaging the product in the most marketable way possible. More accurately, these oils should be called seed oils. Canola, sunflower, corn and safflower oils are all made from seeds. You don't see broccoli oil or spinach oil because vegetables contain barely any oil content at all. But "vegetable oil" sounds more healthy and appealing than "seed oil", doesn't it?
The method by which these oils are extracted from the seeds determines how much nutrition (or harmful elements) is in the oil. As discussed in an earlier post, chemical extraction is the most common and the most harmful way. You want to look for "cold pressed" or "expeller pressed".
There actually is a difference between cold- and expeller-pressed oils. According to this article I found by Spectrum Organics, "All cold pressed oils are expeller pressed. But all expeller pressed oils are not necessarily cold pressed. It all has to do with temperature." You should read the article yourself for more details.
The interesting thing is that the term "cold pressed", while strictly regulated in Europe, is very loosely used in the U.S., often erroneously and in a misleading manner. It's hard to go by what the label tells us sometimes. The phrase that we want to look for then is "unrefined". Refining is the process where they treat the oil in all sorts of horrendous ways (mentioned in the previous post about oils), so a bottle marked "unrefined" would be the way to go.
Manufacturers are always trying to trick us for a profit by finding labeling loopholes. It's up to us to be smart and know what to look for.