Is there any difference between:
There is not a clearer explanation than yours on this matter.
There is no explanation clearer than yours on this matter.
Are they both commonly used to express the same meaning?
The first expression sounds old-fashioned, but they both mean the same thing. The likeliest expression is one you didn't list, with the comparative adjective preceding the noun, "no clearer explanation".
Here is an ngram of the three expressions "no clearer NOUN, no NOUN clearer, not a clearer NOUN_," showing occurrences in books (there are no examples of "not a clearer NOUN"):