Trying to add a hotmail to another hotmail

[IHaveAQuestion]

I have two options at this point:

Send email using your provider's server (recipient will not see your Outlook.com address)
Send email using Outlook.com's server (recipient may see your Outlook.com address)

My question is, if the recipient doesn't see my Outlook.com address, then what do they see?

If you have time, I also need to fill in another question. It is:

Outgoing (SMTP) server: what is it?