In database Design the user of 'fed' compared with login 'fed'.
USE [Design]
SELECT l.name AS login_name, p.name AS [user_name]
FROM sys.sql_logins l JOIN sys.database_principals p ON l.SID = p.SID
WHERE l.name = 'fed'
Why the request under login of 'fed' on the Design database select 'dbo'
USE [Design]
SELECT USER AS user_name
Read this first: CREATE USER
You are confusing LOGIN with USER. Your first query is inspecting LOGIN information, whereas the second is looking at USER. Multiple LOGINs can map to a single USER, which makes things easier to manage, such as administrators all mapped to the database-owner user 'dbo'.
EDIT
Just to clarify, just because you named the column as user_name p.name AS [user_name]
doesn't mean it is. You're linking via sys.sql_logins, so the 'principal' that you are retrieving is the login object, who's name
property is obviously the login name, not the user
.