Puppy Linux offers a few different releases.
The first is an Ubuntu based release called Tahrpup, by using this version the user is able to take advantage of all software and support from Ubuntu.
The second version is called Slacko, which is built upon the Slackware binaries.
The third is called Wary and it is built to support older hardware than the rest.
And the fourth is called Quirky, which is used as a base to explore new ideas.
A portable version, that can be carried on a thumb drive without requiring installation, weighs less than 100MB; a Live CD - less than 150MB. You can even save your settings and files for Puppy on the external device/media.
Running off a live CD also has security benefits, as your system will reset to the known config after each boot.
Using puppy makes you feel like you just jumped 20 years into the past. Being that the purpose of Puppy Linux is to run or really low resource machines the software used is often on the older side, which is precisely why it has a 20 year old look.
Porteus runs a lot of modern apps.
It is based on Slackware, and most any Slackware package can be made into an XZM module that Porteus can load from a USB flash drive. It is fairly simple to put such modules -- or other changes to system configuration files or user files -- in certain directories on your flash drive so that the changes become permanent across reboots, despite the fact that Porteus runs entirely in RAM.
But you can augment the software included by default with other Slackware packages. Regardless, it is not and will not be as featureful as, say, a full traditional installation of a debian/ubuntu/mint distro.
Tiny SliTaz is even smaller than SliTaz and it's built for systems with true minimal requirements. With a size of just 4MB it can fit in a floppy disk.