kurnyb-
I'm not big time savvy either ... and new to Droid from iPhone, but from what I understand about email accounts, the difference is whether you have an iMap account or a POP account. iMAP accounts delete from the server when you access and delete it from anywhere (desktop, phone). POP accounts stay on the server depending on how you have the Preferences set, e.g., Remove from the server after retrieving a message when moved from the Inbox, Remove immediately, Remove in a day, a week, a month, or never. You select in the Account Preferences.
If I don't have it exactly right, I hope someone will chime in.