Prob a bit of both really. Stand up and check your pulse. Then Sit down, then lie down. It's easier for the heart to pump blood when you are lying down, so that will be the lowest of the 3 heart rates.
Running is hardest as you support your weight and use more muscles, and your heart pumps against gravity.
Cycling - mainly your legs, but you aren't horizontal.
Swimming - erm, you are horizontal, so its easier for your heart. And maybe water resistance stops you working as hard as you want to ? (guess - I know nowt about swimming)
If you look at www.polar.fi - there's a whole mine of info about HR.