I sometimes write email when I'm offline using Outlook 2010. The "default" is my personal Outlook account. Although the "From" box has an arrow, shows my business Gmail account and shows "From" Gmail account when I click it, when the specific email arrives it always shows the default personal Outlook email address, not the business Gmail business address I want to send from! This is a problem - I don't want clients having my personal email and, if I switch to the Gmail address as the default, my friends are confused.
I do not have this problem with Outlook online; I am able to switch senders and it comes through correctly.