Yes and no. It really depends on the manufacturer and how they plan on describing the color. Amethyst is basically a light purple, as is violet, but with purple they will usually be referring to a darker purple, usually used for costumes and Halloween type situations.
The Amethyst contacts actually get their color description from the Amethyst stone, which is, you guessed it, purple. By looking at pictures of Amethyst stones you will realize there really is no difference. Many contact lens dealer will use this term as a more elegant way of saying purple, as is the same as when they use violet.
If you have dark eyes, you will almost always want to go with the dark purple contact lenses, as the lighter violet and most amethyst colors will not do anything, or enough to be noticed for your dark colored eyes. Costume contact lenses are perfect for those with dark eyes, even if you plan on wearing them under normal circumstances, day-to-day, etc.
Violet contact lenses will usually be used by lighter-eyes, simply because many times they will be the lighter shades, just used for tint and tone. Not everyone who is interested in violet contacts will want to change their eye color so dramatically that they stand out. Many just use it to accessorize or bring a little flare to their appearance.