i first ran slackware about 2005 i think it was. tgz was also commonly used for gzipped tar archives. debs and rpm files are also tgz internally, i think, maybe they migrated to also supporting bzip2 and xz, with a different header. appimages, snaps and flatpaks are a similar format except with an embedded filesystem, i think at least one of them uses the same squash format as used with initrd. squashfs. there is a driver in the kernel that can mount these, though now there is drivers for all of them, i forget when that appeared, maybe around 2008-2010.
the chances that someone passes you a tgz now are pretty low. at one time, bz2s were called tbz. after that the double extension became more common like tar.xz or tar.bz2, or tar.gz.
nothing to beware of. it's a unix filesystem. you can manually install the slackware packages literally by just doing "tar xvf filename.tgz" at /. slashdot. the root filesystem.