In general:
You have two e-mail accounts setup on your computer. You send two e-mails to me, one per account.
If I look at the "headers" of the e-mail (in Outlook it's normally something like open the e-mail and then click view/options.) In there I'll see things like the IP but (and this is the bit I'm interested in) if you've named your computer something, the name of your computer will be in there. This is how I differentiate between who sent the e-mail (for example, two computers attached to the same network will both use the same IP as the firewall/router/etc) but will have a different computer name.
Know what I mean?
PS Sorry for the terrible grammar in this post, I'm a tad hungover...