Generally tar.gz or .tgz extensions tell you the file is a tar bundle that has been compressed.
You can see what is in the tar bundle with "tar tvf <filename>".
You can extract what is in the bundle with "tar xvf <filename>".
Slackware package management appears to be based on above file naming.
Have a look at this site:
https://www.linux.com/learn/intro-sl...age-management
Having said that however, not all .tar.gz/.tgz packages were created just for Slackware. Many are simply meant to be extracted or extracted, configured and built with make. Usually such packages will have README files in them to tell you what to do after extraction.
Note the i586 in the one package name indicates it is designed to run on 32 bit x86 system (as are i386 & i686). The equivalent 64 bit package would usually include x86_64 rather than one of those. Usually you can run 32 bit apps on your 64 bit system (alongside your 64 bit apps) but if your system is 64 bit you should prefer 64 bit packages to 32 bit unless you have a specific need for 32 bit.