Brownrice uses AWStats for its base traffic analysis with a pretty overlay.
AWStats pulls its numbers directly from your server's logs and does not filter anything. So every human, hacker, and monitoring service is going to show up as a visit (bots are filtered from visits in AWStats but still displayed a separate area.)
That said, GA is much more of a "traffic analysis tool" while AWStats is more of "log analysis tool." i.e. The super smart folks at Google are likely to be doing a lot of good interpretation of what real traffic patterns are like on your web site - while AWStats is going to show you *everything* that is touching your web sites - bots, hackers, everything. AWstats better for showing things like your true bandwidth usage, etc., while GA is going to give you a clearly idea of what real humans are doing on your site.
So the answer is: Yes, the numbers are different.
Here's another fairly detailed comparison of the two tools: