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The difference is the native Box app is going to actually sync whatever is on your Box account into the Box folder on your Mac. The files will actually reside on your Mac as well as on the Box servers.

The second method using Finder does not sync files from the Box server to your Mac. The files will only exist on the Box servers and you will just be using that setup in Finder to view what is on the server. If you wanted a file from Box on your Mac you would need to manually open the Finder connection and drag the file to a local Finder folder so it is downloaded and stored on the Mac.
 
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