When two platforms compete, they’re usually not so closely affiliated. That’s not the case when it comes to WordPress which promotes both WordPress.com and WordPress.org. The former is the one that has millions of free and occasionally paid bloggers using a toned-down version of the master software. The latter is the version that is software only; users have to provide their own hosting and maintenance.
It really comes down to your needs. The convenience and simplicity of WordPress.com is great for casual bloggers who aren’t trying to make a living off of it. Installing the WordPress software onto your own servers with WordPress.org is for “serious” bloggers or businesses. Here’s an infographic from ToMakeAWebsite.net that breaks down the differences.