Regular software is where it must be installed on your computer for it to be able to run. This type will usually have more features or options.
Portable software doesn't install on your computer for it to run. It could run from a standalone .exe file say on your desktop, or from a USB flash drive. This makes it a portable/standalone program, thus the name. This allows you to easily run the program from any computer without it being installed on the computer.
It really just depends on your needs for which one may be best for you.
Hope this helps,