Connecting with a user which has SYSDBA privilege, you act like SYS user

bash-3.2$ sqlplus "/as sysdba"

SQL*Plus: Release 11.2.0.1.0 Production on Thu Jul 23 11:12:10 2015

Copyright (c) 1982, 2009, Oracle.  All rights reserved.


Connected to:
Oracle Database 11g Enterprise Edition Release 11.2.0.1.0 - 64bit Production
With the Partitioning, OLAP, Data Mining and Real Application Testing options

SQL>
SQL>
SQL> show user
USER is "SYS"
SQL>
SQL>
SQL>
SQL> show parameter REMOTE_LOGIN_PASSWORDFILE

NAME                                 TYPE        VALUE
------------------------------------ ----------- ------------------------------
remote_login_passwordfile            string      EXCLUSIVE
SQL>
SQL>

SQL>

SQL> select * from v$pwfile_users;

USERNAME                       SYSDB SYSOP SYSAS

------------------------------ ----- ----- -----

SYS                            TRUE  TRUE  FALSE

SQL>

SQL>

SQL>

SQL> create user admin identified by admin;

User created.

SQL> grant sysdba to admin;

Grant succeeded.

SQL> grant dba to admin;

Grant succeeded.

SQL>

SQL> select * from v$pwfile_users;

USERNAME                       SYSDB SYSOP SYSAS

------------------------------ ----- ----- -----

SYS                            TRUE  TRUE  FALSE

ADMIN                          TRUE  FALSE FALSE

SQL>

SQL>
SQL> grant sysoper to admin;

Grant succeeded.

SQL> select * from v$pwfile_users;

USERNAME                       SYSDB SYSOP SYSAS
------------------------------ ----- ----- -----
SYS                            TRUE  TRUE  FALSE
ADMIN                          TRUE  TRUE  FALSE


SQL>conn admin/admin
SQL> show user
USER is "ADMIN"
SQL>
SQL> select * from v$tablespace;

       TS# NAME                           INC BIG FLA ENC
---------- ------------------------------ --- --- --- ---
         0 SYSTEM                         YES NO  YES
         1 SYSAUX                         YES NO  YES
         4 USERS                          YES NO  YES
         3 TEMP                           NO  NO  YES
         6 EXAMPLE                        YES NO  YES
         5 UNDOTBS2                       YES NO  YES

6 rows selected.

but when you go to shutdown  databasethen use sysdba role

SQL>

SQL> conn admin/admin as sysdba

Connected.

SQL>

SQL> shut immediate;

Database closed.

Database dismounted.

ORACLE instance shut down.

SQL>

SQL> conn admin/admin as sysdba
Connected.
SQL> show user
USER is "SYS"
SQL>
SQL>

if use without  as sysdba so you got ora error

SQL>

SQL> conn admin/admin

Connected.

SQL>

SQL> shut immediate

ORA-01031: insufficient privileges

SQL>