.zip == standard zip compression, like WinZIP. "unzip filename" should pop it open.
.tar.gz == gzipped tar file. "tar -zxvf filename.tar.gz" will pop it.
.tar == regular tar file. "tar -xvf filename.tar" will open this one.
Tar *used* to be primarily for backing things up to tape. Anymore, it's mostly used to turn a whole pile of files (like a directory) and make them one file.
gzip and zip are just different compression methods.
tar.gz is the most common one you'll run into.
.rpm is RedHat's package manager (rpm, get it?) SuSE, Mandrake and some others use it too. "rpm -i filename.rpm" should install it.