How to build a simple blog where content could be published securely to user groups?
As per your "... there could be other distributions or modules that I don't know about too." in your question: have a look at the Group module (commonly perceived as an alternative for Organic Groups).

Group allows for creating arbitrary collections of your content and users on your site, and grant access control permissions on those collections. It is available as of D7, and has a D8 version also. The Group module creates groups as entities, making them fully fieldable, extensible and exportable. Which also makes it integrate very well (out of the box) with commonly used modules such as Rules, Views, etc.

Some more questions you may want to look at for more details:


What are the various roles supported by the Group module?, which explains the various types of roles that can be used. 
How to bulk assign existing content to a group created with the Group module?, a typical issue when adding this module to an existing site).
What are the features of the Group module versus Organic Group module?


Resources


Community documentation for the Group module.
Video tutorial "How to use the Group module in Drupal 8 to manage editorial access control to different areas of a web site".