Difference EXECUTE AS targets - sql-server

Question

I am not quite clear about the difference between different EXECUTE AS targets in SQL Server : CALLER, SELF and OWNER, notably between the last two.
My understanding is that CALLER is the one who Execute/Call the procedure.
SELF is the specified user is the person creating or altering the module
OWNER is the current owner of the module
Could you explain and give some example who is the person creating/modifying and the owner of the module. Is 'module' here the stored procedure/function or the session or the database ? Including an example with SELF user will be great.

Answer 1

Being put very simple, SELF impersonates you as a database user who actually executed create / alter procedure the last time. It doesn't always have to be the schema owner, as you can imagine, it can be any person with permissions sufficient to create / modify given objects.
The OWNER mode impersonates you as the owner of the schema the procedure / function belongs to.
If you want to dig a little deeper (and is this case, there is always some room to dig in), below is a (relatively) simple example that can demonstrate you how things can work here. There are some shortcuts and implications that are specific to SQL Server which I omit deliberately because otherwise it would be too much to write. You can always read the documentation, though.
use master;
go
if db_id('TestDB') is not null
drop database TestDB;
go
create database TestDB;
go
use TestDB;
go
-- Just for the sake of example, so that everyone can create procs
grant create procedure to public;
go
-- Schema owner
create user [SomeUser] without login;
go
create schema [s1] authorization [SomeUser];
go
-- An ordinary user
create user [AnotherUser] without login;
go
grant execute on schema::s1 to AnotherUser as [SomeUser];
go
-- Database administrator
create user [DBA] without login;
go
alter role [db_owner] add member [DBA];
go
-- Although it's SomeUser that owns the schema, DBA creates objects in it
execute as user = 'DBA';
go
create procedure s1.SpCaller
as
select user_name() as [s1_caller];
return;
go
create procedure s1.SpSelf
with execute as self as
select user_name() as [s1_self];
return;
go
create procedure s1.SpOwner
with execute as owner as
select user_name() as [s1_owner];
return;
go
revert;
go
-- You can play with actual impersonation and look at results
execute as user = 'AnotherUser';
go
exec s1.SpCaller;
go
exec s1.SpSelf;
go
exec s1.SpOwner;
go
revert;
go