Although Caryn is usually a form of Karen, often Welsh parents connect it to "caru", so it's related to Carys. I love this name! It's so gorgeous -- all of the "caru" names are, IMO. Is it pronounced KA-ris or ka-RIS? I love it either way.
It doesn't mean love in Welsh, it actually means "my loved one". It's a really old fashioned name, the Welsh equivalent of say Edith or Ethel. Ancient almost.
Actually, Carys is a very modern Welsh name, compared to something like Edith, which is over 1000 years old. It's an invented name, based on caru + the -ys ending common in popular names like Dilys and Gladys. According to the British birth records, it was first used in 1903, but was very rare until the late 1940s /early 50s, and hasn't really been popular until relatively recently. In 2010 it was #45 in the Welsh name charts, so, um, yes, sorry first poster, Welsh people do use it and it's not old-fashioned. I think you must be confusing it with Gladys or Dilys or Nerys. [noted -ed]
I wouldn't say this name was related to either Ethel or Edith which, in spite of their Old English roots, are themselves unrelated, as Ethel means "noble" and Edith means "prosperous strife".