Community support is, for example, what you get here on LQ: Free support & help, provided out of the good of our hearts
to our fellow Linux users. The key part is it is free, and there are millions of people hanging around willing to help.
Commercial support is loosely defined as "..support for which you pay money" such as what a large company might want for their huge number of servers or other computer systems. Examples of commercial support would include that which is provided for enterprise customers who pay for support for Novell, SuSE Linux (SLES or SLED), or RedHat Enterprise systems (RHES or RHEL), or Windoze server systems.
Not every Linux distro, or probably even very many at all, offer commercial (as in PAID FOR) support. The whole idea behind free & open source community driven software like Linux, is the community that provides support.
As to which is 'better' for this or that, I suspect it is a very subjective opinion.
If you are a business with giant numbers of systems and you want 24-7 support for upgrades, troubleshooting, etc., then you may want to opt for a paid support system.
Contrarily, a desktop user like me would sooner chop off my hands than pay for support for my one desktop computer, because I can generally figure out my own solutions to issues, or come here or to many other community support places and seek help.
I'm sure you will get more detailed info from other users, as well as opinions as to which is better for what.