The versions released on WordPress.org, which can be downloaded and installed on any server, are developed and maintained by me. The versions released on WordPress.com, which is a paid service maintained by Automattic, are developed by Automattic based on the original designs.
They mostly look and work the same, but there are some differences in functionality. If you’re using one of my themes on WordPress.com and want to use that same theme on a self-hosted server, I can’t guarantee that you’ll be able to retain all of the features you're used to. Mostly because a lot of those features are tied into the WordPress.com service itself, rather than a specific theme.
If you have a question about a theme on WordPress.com, you should post a message in the WordPress.com support forums. If you have a question about a theme for the self-hosted version of WordPress, you should post a message in the WordPress.org support forums.