|Bzip2 consumes far more CPU cycles than gzip in order to produce its (sometimes considerably) smaller files.|
Also, both gzip and bzip2 will accept data from standard input so that you can use them as filters. This is useful for speeding up the compression of program output -- and is also quite handy when you don't have enough disk space for both compressed and uncompressed copies of a file.
In *nix land, bz and gz are two of the most common compression formats. Typically you use the bzip2 utility to create bz files and gzip to create gz. The fundamental difference is in the compression algorithm used by bzip2, which results in considerably smaller files. The downside is that bzip2 eats up more memory.
To compress a file using gzip, use the command gzip filename . The result is a file named filename.gz. Thus the command gzip homepage.htm yields homepage.htm.gz.