Step 1: Separate joining rope to rope from joining rope to a fitting.
Capping, recapping, and socketing all describe attaching some external hardware, a cap or socket, onto the end of a rope so that it can be connected to a cage, skip, or other equipment. None of these methods join two lengths of rope directly to each other.
Step 2: Picture what happens when two rope ends are joined without any hardware.
To join two ropes permanently and seamlessly, the strands at each rope's end are untwisted (unlaid) for some length, and then the loose strands from one rope end are woven back in among the strands of the other rope, following a set tucking pattern, so the two ropes effectively grow into one continuous piece.
Step 3: Name this technique and its typical use.
This weaving together of strands is called splicing. It produces a joint only slightly thicker than the rope itself and is the standard method for making the continuous, endless loop of rope used in endless rope haulage systems, since there is no separate fitting to catch on anything as the loop travels around the system.
\[ \boxed{\text{Splicing}} \]