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Tar is originally based on 'tape archiving' - still does that, but it's mainly used to bundle up many files into one. zip, gzip, and bzip are all compression utilities, using different algorithms. So a *.tar.gz is a file that has been gzipped and tarred. To extract it,
tar -xzf file
If it's been bzipped, it's
tar -xjf file
If it's been zipped, I usually do 'unzip file'.
Man tar (and all the rest for more details.)
-- Actually, to be a little more precise, bzip is a better algorithm - compresses more - but takes longer to compress and extract. gzip is pretty good and faster. But, on most processors, .005 seconds and .007 seconds isn't much to get excited about. Then again, with today's hard drives and DSL, 250k and 230k (I'm making up numbers - I'm not sure what the actual average ratio is) isn't much either.