One of those wonderful common points of confusion...
A "tarball" is slang for any archive generated by the TAR utility (file extension .tar). These can also be compressed with GZIP (.gz extension), or BZIP (.bz extension)
So you can have files ending in .tar , .tar.gz (or .tgz), tar.bz, .gz , or .bz
ANY of these can contain application, source code, or pictures of your kids. You don't install these, you uncompress them, unpack them, etc.
Package managers have their own extensions---eg .rpm for the RPM package manager. These file are typically opened using the package manager SW, as in "rpm --install someapp.rpm"
The unpacked archive could also contain source code or executables. In both cases, there would likely be additional instructions for install and setup.
Always start with your package manager in the GUI. Once you know about repositories and such--and you know the name of an application, you can get it on the command line. Documentation includes man pages--eg "man rpm"