Save File On External Drive Not The Same As Internal Drive

Why do files moved to an external drive not behave the same as those same files in an internal drive? I noticed that if I do anything to a file that is in an external drive, that file can not be saved under the same name (read only). In order to do so one must save it internally and then copy or move it to the external drive. So I did just that--I copied a file from taken from an external drive, saved it in the internal one and then copied it back to the external one. Now if I r-click the propeerties of these 2 same files and then go to the 'Security' tab a difference is immediately apparent: The internal one has -1- System & -2 My-computername (user-PCuser and -3- Administrators (user-PCAdministrators) with all 3 accounts allowing all (full control, read, write, etc..). While the external drive has in Properties; -1- System -2- Administrators (user-PCAdministrators) and -3- Users (user-PCUserrs) with this final 3d one (and different one) with no Allow for "full control, or modify or write. So how does one have all its files in this external drive behave and be equal to all the same files in the internal drive? Since -3- Users (user-PCUserrs) in the external drive is that which is differnt from the internal drive I was wondering if it is OK to delete this Permission or 'attribute' or whatever it is called and create instead one equal to the one in the internal drive -3- Administrators (user-PCAdministrators)? ANd of course doing so in one go and not file after file after file, individually, would be ideal.