I don't think the Mac App Store differentiates between installed vs purchase & installed. I have a few apps such as the iWork '09 one that were installed long before there was a Mac App Store & several I've purchased through the Mac App Store. All of them say "Installed" although there are many that are available in the Mac App Store that I purchased previously that don't show "Installed."
I read some where that that has to do with how the programmer codes the store listings but I'm not clear on the details. I have a couple of apps that show as Installed & the developer clearly states on their web site that the two, Mac App Store & separately purchased, are not interchangeable.