Close, although not exactly the same. One of the buildings within the Quincy Market complex is called North Market, so I understand the confusion. The area you want is called the North End... it's a section of Boston with a lot of history (the Freedom Trail runs through it) and some wonderful Italian restaurants. We actually do some of our grocery shopping there.
It's not a very far walk from Quincy Market to the North End... just follow the red line on the sidewalk that marks the Freedom Trail. Just ask one of the Rangers to point you in the right direction, as the Freedom Trail is one large loop.