They are 4mm smaller in radius, 8mm smaller in diameter.

700c (622mm) tires will not fit on 27" (630mm) rims. I would love to watch someone manage to get a 700C tire onto a 27" rim, and if they managed to stretch it over the rim sidewalls, try to have it inflate properly - but I only want to see this for the comedic value.

If the 27" rims are damaged, you can often upgrade to 700c rims if your brakes can be adjusted 4mm down in their slots on the brake calipers. This also gives you an extra ~4mm of tire clearance, so a bike that originally came with 1-1/4" (~32mm) wide tires can often fit up to 35mm or 38mm with 700c wheels. If you can't adjust your brakes that much, 27" rims are still available, both new cheap replacement rims and better quality ones on the used market.

And Panaracer Pasela tires are the best option in my opinion. I think there are also a couple options from Continental, and a few others. I use Paselas on my 700c wheels, not because there are few options, as with 27", but by choice because they are excellent performers and good value.