SQL server,What's the difference between the database OWNER and login user MAPPING? and How can I add the SCHEMA?

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SQL

SQL-Server

I am using SQL Server 2008 R2.

TEST 1:
step 1. I create a login user named 'mtcs', just a user ,no database mapping.

step 2. I create a database named 'DBMTCS', and ,I assign the 'mtcs' as owner to database 'DBMTCS'.

step 3. After step1,2, I want change the schema from the User Mapping of the user 'mtcs' ,but can not.


TEST 2:
step 1. I create a database named 'DBMTCS', the owner is default.

step 2. I create a login user 'mtcs', than I do the user mapping, I changed the schema of 'DBMTCS'.

step 3. I change the owner of 'DBMTCS', but can not.

Before this test, I just want to create a database which has its own user and schema.Still not complete. so there I have 2 questions:

1.Whats the difference between the database OWNER and login user MAPPING?


2.How to change the schema of the database?



Thanks in advance