1995 Mercury Mystique GS my cooling isnt running BUT,,,?

if I take the relay out and put in the high speed relay slot the fan kicks in on high speed and the relay is buzzing then I put back in regular speed relay slot and regular speed works but when I shut engine off it keeps running and running after engine is cool. So I take the relay out and put back in it runs I tapped it and it stopped I was wondering if there is something that controls relays that is working or is it the relay I have no idea I hope someone knows there stuff. I sure dont...lol