Files with same content but with different md5sums when gzip'd?

I don't know why this is happening, but I upload some files to Amazon S3 then delete the sent files checking their md5sum both in Amazon and locally. But recently I found this issue about the same content are generating two different md5sum

[valter.silva@alog ~]$ ls
renew.log  s3

[valter.silva@alog ~]$ ls s3/
renew.log

[valter.silva@alog ~]$ md5sum renew.log 
d41d8cd98f00b204e9800998ecf8427e  renew.log

[valter.silva@alog ~]$ md5sum s3/renew.log 
d41d8cd98f00b204e9800998ecf8427e  s3/renew.log

[valter.silva@alog ~]$ gzip renew.log 
[valter.silva@alog ~]$ gzip s3/renew.log 

[valter.silva@alog ~]$ md5sum renew.log.gz 
aa1f0ae9a61aac5bcd32b917fbd9324b  renew.log.gz

[valter.silva@alog ~]$ md5sum s3/renew.log.gz 
6ae0e48edb68e9ed938fdfc3894f6c94  s3/renew.log.gz

Does anybody knows why that's happenning ? Or how should I check if my files are consistent, reliable ?

update Answering Tiago Cruz answer:

[valter.silva@alog ~]$ sha1sum renew.log 
da39a3ee5e6b4b0d3255bfef95601890afd80709  renew.log

[valter.silva@alog ~]$ sha1sum s3/renew.log 
da39a3ee5e6b4b0d3255bfef95601890afd80709  s3/renew.log

[valter.silva@alog ~]$ gzip renew.log 
[valter.silva@alog ~]$ gzip s3/renew.log 

[valter.silva@alog ~]$ sha1sum renew.log.gz 
2d9111d9db71da9fe4de57fbc19c89eb0bd46470  renew.log.gz

[valter.silva@alog ~]$ sha1sum s3/renew.log.gz 
05014ca24d133f1761f9134e8dab52e6e2111010  s3/renew.log.gz

It gives the same problem Tiago.

According to RFC 1952, the gzip file header includes the modification time of the original file (field MTIME). You can display the header in plain text¹⁾ with gzip -lv renew.log.gz:

method  crc     date  time           compressed        uncompressed  ratio uncompressed_name
defla 64263ac7 Jun 21 17:59                 314                 597  52.1% renew.log

So, if you really want to compare the gzip'd files, compress them with the -n option, to not save the original file name and time stamp,

gzip -n renew.log s3/renew.log 

and their md5sum should be identical.

Otherwise you could use

md5sum <(zcat renew.log.gz) <(zcat s3/renew.log.gz)

to calculate the md5sum of the decompressed files.

¹⁾ However, the displayed time and date are not taken from the header, but represent the current values; this is also the case for the file name:

$ gzip renew.log 
$ mv renew.log.gz foo.gz
$ gzip -lv foo.gz -------- uncompressed name is taken from current name ---v
method  crc     date  time           compressed        uncompressed  ratio uncompressed_name
defla 6c721644 Jul 11 22:34                 580                1586  65.7% foo
$ hexdump -C foo.gz | head -n 2
00000000  1f 8b 08 08 f0 16 df 51  00 03 72 65 6e 65 77 2e  |.......Q..renew.|
00000010  6c 6f 67 00 8d 93 dd 6e  9b 30 18 86 8f 89 94 7b  |log....n.0.....{|
                                                             ^^^-------^^^^^
                                                  original filename is stored in the header

Why do you expect compressed version of the same file to be the same? The compress program (gzip) can include some timestamp in the header, or can use some randomized algorithms.

And exactly! The gzip header contains the timestamp. If you want your compressed files to be the same, your file has to have the same timestamp!

So, when you copy a file, always do it as cp -p file1 file1, not just cp file1 file2 - that is actually a bad habit!