A facilities based CAP, or Competitive Access Provider is similar to a CLEC established, owned, and operated as a competitor to the Incumbent Exchange Carriers. CAPs provide their own access facilities infrastructure. Many established their own competitive local exchange facilities too, independent from the major ILEC carriers.
A non-facility based CLEC is a competing carrier who is leasing from one of the incumbent carriers, or even from another CLEC.  A CLEC can establish a reseller relationship with an ILEC or a CAP.