Is there a difference between pure binary and binary?
I'm guessing here for lack of context, but I think the following distinction is reasonable.

A binary encoding is anything that maps stuff to bit strings. There are many, including two's complement, IEEE float, ASCII, and so on.

Pure binary probably refers to bland natural numbers written in base two, i.e.
if $n_{(2)} = a_k\dots a_0$ then

$\qquad\displaystyle n = \sum_{i=0}^{k} 2^ia_i$.