Hi,
Yes in theory they should be the same but apparently in practice they are not since occasionally people report problems with the download link. I recommend use Tortoise HG, I have no control over whether the download links that codeplex generates for source code are complete. They generate those links from the repository somehow but they also support Team Foundation server in addition to Mercurial for source code repositories. I guess they don't have it perfected for Mercurial.
The only thing I can do is report it to the codeplex team, but to be sure you get the complete source code the best solution is to just use Tortoise HG. This also makes it easy to get updates on a daily basis or as often as you want to.
Best,
Joe