We have documentation for this here:
https://help.runbox.com/aliases-profiles/
The biggest difference is that you can specify a different name with a profile, and also a non-Runbox address. It has to be verifiable otherwise we would be allowing people to send from someone else's address without their permission.
The only common elements in mails sent from our service are the servers (which you would expect) and the fact we include your numerical User ID in outgoing headers. If someone happened to have two emails sent from different aliases/profiles on your account and looked at the headers they might be able to accurately conclude the emails might be from the same sender. The way around this is to purchase a sub-account which would have a different UID.
I hope that helps.