Hot backups are when database is up and running you take backup(DB has to be in archivelog mode in order to do that.) Cold backups are shutdown the database and copy datafiles control files and save them some place safer(on a different server) Good dba should do that atleast once a month. When you rman backups benefit is that it only backsup blocks that have been used empty data does not get backed up. This is very efficient as far as space issues go.
1. Hot inconsistance and online backup are same 2. Cold close consistance and offline backup are same
For 1. db must be archive mode inconsistance mean the SCN are not same For 2. db may be archive mode consistance mean SCN are same (controlfile datafile)
Logical backup through import/export utilities Physical backup simply copy all file using OS command
