Otherwise known as "jack".

Not to be confused with "the jack", as described by AC/DC

AS far as the stones go, personally I'd use the synthetics for setting up razors and the naturals for maintaining them. Unless you don't care about the particular razor too much. There is some satisfaction that comes with shaving 500 times with a razor and seeing no visible wear.

I much prefer a fine natural and a single (tomo)nagura to fine synthetics, but my tune would probably be different were I honing for pay.

With good leather and a good linen, the stone can literally be a place you take a razor once every 6 months, and without any compromise in sharpness (you may find that the sharpness drops with a honing). With a bad linen, that won't be true, though.