No, you can use the same relay.
If earth switched you wire the relay coil to the live side of the horn switch - so from +12V supply, to relay coil, from relay coil to horn switch, to earth.
If live switched, you put the relay on the earth side of the horn switch. Don't think I need to spell that one out
I removed the cheapo air horns from RTA and fitted some Fiamm bike horns as fitted to BMW, Guzzi etc. The air horns were pretty naff TBH so a return to a pair of good 'old fashioned' loud twintone horns is a nice change. Much of the original wiring was still in existence, but I replaced the horn wiring from bulkhead forward, including fitting a relay on the bulkhead. My car is much older of course!
Cheers,
