Diffrences between master and slave replication in mysql?

In a database named asterisk, there is a table named cdr which was partitioned on the time field.

mysql> show create table cdr;
Create Table: CREATE TABLE `cdr` (
`gid` bigint(20) NOT NULL AUTO_INCREMENT,
`id` bigint(20) NOT NULL,
`start` datetime NOT NULL DEFAULT '0000-00-00 00:00:00',
`clid` varchar(80) NOT NULL DEFAULT '',
`src` varchar(80) NOT NULL DEFAULT '',
`channel` varchar(80) NOT NULL DEFAULT '',
`duration` int(11) NOT NULL DEFAULT '0',
`billsec` int(11) NOT NULL DEFAULT '0',
`disposition` varchar(45) NOT NULL DEFAULT '',
`uniqueid` varchar(32) NOT NULL DEFAULT '',
`dnid` varchar(20) NOT NULL DEFAULT '',
`line` varchar(20) NOT NULL DEFAULT '',
`prefix` varchar(20) NOT NULL DEFAULT '',
`service` varchar(100) NOT NULL DEFAULT '',
`cost` int(11) NOT NULL DEFAULT '0',
`visit` varchar(500) NOT NULL DEFAULT '',
`pressed` varchar(200) NOT NULL DEFAULT '',
PRIMARY KEY (`gid`,`start`),
UNIQUE KEY `id` (`id`,`prefix`,`start`),
KEY `start` (`start`),
KEY `clid` (`clid`),
KEY `service` (`service`)
) ENGINE=InnoDB AUTO_INCREMENT=40086530 DEFAULT CHARSET=latin1
/*!50500 PARTITION BY RANGE  COLUMNS(`start`)
(PARTITION p0 VALUES LESS THAN ('2013-11-16') ENGINE = InnoDB,
 PARTITION p1 VALUES LESS THAN ('2014-01-20') ENGINE = InnoDB,
PARTITION p2 VALUES LESS THAN ('2014-02-20') ENGINE = InnoDB,
PARTITION p3 VALUES LESS THAN ('2014-04-01') ENGINE = InnoDB,
PARTITION p4 VALUES LESS THAN ('2014-06-01') ENGINE = InnoDB,
PARTITION p5 VALUES LESS THAN ('2015-01-01') ENGINE = InnoDB,
PARTITION p6 VALUES LESS THAN (MAXVALUE) ENGINE = InnoDB) */

I make a slave replication from it to another server successfully.

Since, I check the database files on file system, I saw something incredible. File size of partitioned table differ on master and slave.

Master Server

root@mdb1-msh:# ls -lh /var/lib/mysql/asterisk_archive 
total 12G
-rw-rw---- 1 mysql mysql 1.7G May  8 22:35 cdr#P#p0.ibd
-rw-rw---- 1 mysql mysql 1.7G May  8 22:35 cdr#P#p1.ibd
-rw-rw---- 1 mysql mysql 1.7G May  8 22:35 cdr#P#p2.ibd
-rw-rw---- 1 mysql mysql 1.8G May  8 22:35 cdr#P#p3.ibd
-rw-rw---- 1 mysql mysql 1.9G May  8 22:35 cdr#P#p4.ibd
-rw-rw---- 1 mysql mysql 1.6G May  8 22:35 cdr#P#p5.ibd
-rw-rw---- 1 mysql mysql 916M Aug 18 06:33 cdr#P#p6.ibd
-rw-rw---- 1 mysql mysql 8.9K May  8 21:15 cdr.frm
-rw-rw---- 1 mysql mysql   48 May  8 21:15 cdr.par
-rw-rw---- 1 mysql mysql   61 May  9 10:16 db.opt

Slave server

root@db-ast1:~# ls -lh /var/lib/mysql/asterisk
total 11G
-rw-rw---- 1 mysql mysql 1.7G Aug 17 09:08 cdr#P#p0.ibd
-rw-rw---- 1 mysql mysql 1.6G Aug 17 09:08 cdr#P#p1.ibd
-rw-rw---- 1 mysql mysql 1.7G Aug 17 13:24 cdr#P#p2.ibd
-rw-rw---- 1 mysql mysql 1.7G Aug 17 13:24 cdr#P#p3.ibd
-rw-rw---- 1 mysql mysql 1.9G Aug 17 15:49 cdr#P#p4.ibd
-rw-rw---- 1 mysql mysql 1.6G Aug 17 17:07 cdr#P#p5.ibd
-rw-rw---- 1 mysql mysql 868M Aug 18 00:09 cdr#P#p6.ibd
-rw-rw---- 1 mysql mysql 8.9K Aug 17 05:28 cdr.frm
-rw-rw---- 1 mysql mysql   48 Aug 17 05:28 cdr.par
-rw-rw---- 1 mysql mysql   65 Aug 17 04:47 db.opt

I need to know what's wrong? what are differences? how to do this operations? How to check data-integrity?

UPDATE1

Master

mysql> select count(gid) from cdr;
+------------+
| count(gid) |
+------------+
|   28170822 |
+------------+

Slave

mysql> select count(gid) from cdr;
+------------+
| count(gid) |
+------------+
|   27531422 |
+------------+

and for percona checksum:

user@db:~$ pt-table-checksum h=slave-host,u=root,p=pass --databases=asterisk --tables=cdr
Checksumming asterisk_archive.cdr:   7% 06:19 remain
Checksumming asterisk_archive.cdr:  20% 03:52 remain
Checksumming asterisk_archive.cdr:  33% 02:56 remain
Checksumming asterisk_archive.cdr:  46% 02:18 remain
Checksumming asterisk_archive.cdr:  59% 01:42 remain
Checksumming asterisk_archive.cdr:  72% 01:07 remain
Checksumming asterisk_archive.cdr:  90% 00:23 remain
        TS ERRORS  DIFFS     ROWS  CHUNKS SKIPPED    TIME TABLE
08-18T10:41:34      0      0 27531422     180       0 228.538 asterisk.cdr

UPDATE2

I checked the mysql.err and there were no errors and the below is the replication status:

mysql> show slave status \G
*************************** 1. row ***************************
           Slave_IO_State: Waiting for master to send event
              Master_Host: 192.168.34.20
              Master_User: slave_user
              Master_Port: 3306
            Connect_Retry: 60
          Master_Log_File: mysql-bin.000103
      Read_Master_Log_Pos: 1036136
           Relay_Log_File: mysql-relay-bin.000034
            Relay_Log_Pos: 1036282
    Relay_Master_Log_File: mysql-bin.000103
         Slave_IO_Running: Yes
        Slave_SQL_Running: Yes
          Replicate_Do_DB: 
      Replicate_Ignore_DB: 
       Replicate_Do_Table: 
   Replicate_Ignore_Table: 
  Replicate_Wild_Do_Table: 
 Replicate_Wild_Ignore_Table: 
               Last_Errno: 0
               Last_Error: 
             Skip_Counter: 0
      Exec_Master_Log_Pos: 1036136
          Relay_Log_Space: 1036481
          Until_Condition: None
           Until_Log_File: 
            Until_Log_Pos: 0
       Master_SSL_Allowed: No
       Master_SSL_CA_File: 
       Master_SSL_CA_Path: 
          Master_SSL_Cert: 
        Master_SSL_Cipher: 
           Master_SSL_Key: 
    Seconds_Behind_Master: 0
  Master_SSL_Verify_Server_Cert: No
            Last_IO_Errno: 0
            Last_IO_Error: 
           Last_SQL_Errno: 0
           Last_SQL_Error: 
  Replicate_Ignore_Server_Ids: 
         Master_Server_Id: 513
1 row in set (0.00 sec)