Sliver

 https://en.m.wikipedia.org/wiki/Splinter

The definition of sliver, according to the dictionary, does include that which makes up a splinter.  A small fragment of wood is not a splinter.  A splinter is a very light piercing of the skin from a sliver.  I have lots of slivers, I'd presume anyway, since I don't clean my living quarters very often.  I have had far less splinters.

I find it hard to believe that anyone not stuck 75 miles out in the middle of the woods with no access to TV or radio doesn't have a familiarity with the word "splinter".  Up until recently I was completely unaware that a splinter was sometimes known as a sliver.  If my disbelief is unwarranted, I'd like to know.  Unfortunately it seems I'm mainly just talking to myself here.