Spectral violet and ultraviolet are just two ranges on the continuous frequency spectrum, so they differ in frequency.
There are several different classes of UV light, just like there's many shades of blue or classes of infrared (near, long-wave, mid-wave, etc).
The reason that you can see light from "UV" lamps is because they're usually emitting over a range of wavelengths and some of that falls in the visible spectrum. And on the other end, some infrared LEDs emit a little bit of red light which is visible.
If something isn't visible it matters for safety. Most of your eyes' defense mechanisms rely on limiting the amount of light entering your pupils, so they need to be able to perceive how bright a light is. Strong UV is particularly dangerous because it's high energy (think sunburn) and you can't see it so you won't reflexively blink and your pupils won't close. Infrared can also be dangerous, but it's a lower wavelength so you need more of it to do damage.
It's ultra because it isn't within the visible spectrum. Violet is a spectral color, which means it's evoked by a single wavelength of light. So the term spectral violet refers to all the shades of violet.
>>why does it matter?
You have a word for it.
Some fluorescent materials can be lit with UV light, because they will fluoresce at wavelengths we can see. Otherwise, UV lamps also emit visible wavelengths.
People who have had cornea-replacement surgery and opted for the UV-transparent corneas can see further into the UV.[1] A child (with young corneas that haven't yellowed at all) almost certainly can too.
[1] e.g. http://www.komar.org/faq/colorado-cataract-surgery-crystalen...
The CIE charts don’t really consider how to interpret or recolor data outside the color space, for example the UV reflection from flowers or astronomy photos in the UV/X-ray spectrum.
Do spectral violet and ultraviolet differ? In what way? If something isn't visible, why does it matter?