Very good question!
There are some very minor differences, but for the most part, their purpose is the same. Both of these processors try to stay very close to the original Markdown specification as designed by John Gruber.
The main difference is that "Markdown (Classic)" is the original processor used in MarkdownPad 1 (it was the only processor in that version). MarkdownPad 2 uses the new "Markdown" processor as its default processor, and in case there are any minor differences, both versions are included if users prefer the processor from MarkdownPad 1.
I hope this is clear, please let me know if you need additional information.