I'm not sure as to the origins of clog but I can tell you a bit about the rapper stepping. Traditionally there were many different types of step or shuffle but today, there tends to only be one step or a variant of it. This is the 'Single Shuffle', the most basic step as done by any clog dancer.

The taps come from the ball of the foot, never the heel and the dancer moves from their left to their right foot on alternate beats. Since rapper is only ever performed to 6/8 jigs, then with each beat, there are two extra quavers, the taps are performed as below.

L t t      R t t      L t t      R
1 and-a 2 and-a 3 and-a 4

So the stepping used in rapper came directly from the clog dancers who were around Northumberland/Tyneside at the time of the dances. Some sides did use very complicated Northumbrian clog steps and others used simpler steps. Single shuffles, double shuffles and even more complex stepping patterns were regularly used. Today, you only tend to see single or double shuffles in a rapper dance.

For more info have a look at http://www.rapper.org.uk/

Or for examples of stepping in rapper:
http://www.youtube.com/watch?v=Pf2gQQjSUtk
or
http://www.youtube.com/watch?v=Vu4GDMXjFQs

Ta
Tom