This is NOT a big deal; I'm merely curious.
Both Macs are on Snow Leopard.
One Mac, fire up Mail, and as soon as you do anything including reading an old email, it immediately springs into action and downloads awaiting emails.
The other Mac, fire up Mail, and you have to prod "Get Mail" sometimes twice, to get it to download (the same) awaiting emails.
Some setting or other? Not a big deal, just a weird anomaly.
FWIW I prefer having to make it download emails than the energetic springing into action, action. When I'm on that computer I sometimes miss some.