7zip is more a compactor (like PKZIP) than a compressor. It's available for Linux, but it can only create compressed archives in regular files, it's not able to compress a stream for instance. It's not able to store most of Unix file attributes like ownership, ACLs, extended attributes, hard links...
On Linux, as a compressor, you've got
xz that uses the same compression algorithm as
7zip (LZMA2). You can use it to compress tar archives.
bzip2, there's a parallel variant
pixz that can leverage several processors to speed up the compression (
xz can also do it natively since version 5.2.0 with the
-T option). The
pixz variant also supports indexing a compressed
tar archive which means it's able to extract a single file without having to uncompress the file from the start.
Compact is archive+compress (possibly with indexing, possibly members compressed separately), archiving doesn't imply compression. It is not a DOS thing, but possibly it was a French thing. Googling usenet archives, I seem to only come across articles of mine, so it could well have been my invention, though I strongly believe it's not.