Clutch is a WebUI for the Transmission daemon. It allows you to manage your torrents from anywhere you can access the internet.
Clutch does not interact with the OS X Tramsission.app GUI at all. Clutch comes bundled with transmission-daemon, and does not interact with any desktop Transmission GUI clients (it may in the future, but this is undecided at this stage). Torrents downloaded with Clutch will not appear in Transmission.app.