I've spending most of the week here in chilly Bellevue, WA at the MVP Summit! For this trip, I'm staying connected with my Windows Phone 7 and my new HP Envy X2 with Windows 8. I'm accessing my Gmail account from both OSes and I noticed something interesting with the handling of mail within their individual apps.
On the Windows Phone, the mail application has a trash icon for deleting messages. When I delete from the phone, the API call to Google is "archive" and that message is simply archived and moved out of my inbox.
On the Windows 8 native Mail application, the trash icon sends the API call for "delete" to Google, sending the message to the trash, which is removed after 30 days.
Perhaps the reason is because when you are on your phone, you probably aren't actively "managing" messages and archiving them allows you to remove them from your device, but not really delete them. From your computer, you might be more actively sorting and addressing messages, where a true "delete" function is more desirable. Or maybe I'm over thinking it. Since the applications were developed by different Microsoft product groups, they simply selected different API functions.
While it might be desirable to have the same experience across both of my Windows devices, I can use the difference to my advantage - making sure that my mail ends up where I want it, depending on where I delete it from.