<sigh! @john_mcclenahan posted while I was writing this. Oh well, since it is already done I'll submit it anyway. I haven't taken the effort to assure a 100% correct timeline, so please old-timers don't take me to task . One statement of John's that I would correct is that namespace clashes were and can still be an issue if authors do not follow best practices in their Ruby code. Trimble's Extension Warehouse is pretty strict about good module structure, but plugins from other sources may still be problematic.>
Dave has already addressed most of the mechanics of installing, so for your benefit and any others who might read this, I'll write about some of your other questions.
In the early days of SketchUp, add-ons written using the Ruby API were all called "plugins" and typically consisted of a single Ruby .rb file. The user downloaded them and then installed them manually by copying the Ruby (.rb) file into the Plugins folder (which SketchUp created during installation). There were various repositories for downloading plugins, several of which are still around and active, and also some authors who provided downloads from their own sites.
Over time, several serious issues with this process became evident. Users often had trouble locating the Plugins folder to do the installation. The location was completely different for Mac vs Windows (this is still true). There could be permissions problems with trying to copy a file into the Plugins folder, as it was in a system area that ordinary users don't have permission to write. And, as plugins became more sophisticated, many of them contained multiple files and subdirectories, all of which had to be correctly placed in Plugins. There was a constant stream of issues from people who just couldn't get it to work. Also, particularly in corporate environments, the IT department might have policies restricting what users can and cannot download or install.
Late in the SU 8 lifetime, SketchUp started to make changes to improve the situation. They added a new manager to automate the plugin installation process, so the user wouldn't have to know how to find the Plugins folder. They added the new .rbz file type to better handle plugins that need multiple files and/or directories (though a .rbz can perfectly legally contain a single Ruby file). A .rbz file is just a zip file containing the plugin contents, with .rbz instead of .zip as the file's extension. The different file extension is only to help avoid someone trying to install a zip that doesn't contain SketchUp Ruby code. The new manager knew how to unzip and install files from a .rbz and where the Plugins folder was located.
At some point, they also changed the location of the Plugins folder to be in each user's personal folders instead of the application's folders. This eliminated the issues with permissions because a user always has permission to access their own folders. But on both Windows and Mac, the standard location of SketchUp's user-support folders is hidden by the OS by default. The problem of users not being able to find the Plugins folder remains to this day! But, since one is now expected to use the manager instead of doing the install manually, this isn't deemed to be the problem it once was. It it still possible to download a plugin from an arbitrary site, and if it is packaged in a .rbz, the user points SketchUp's manager at the file to install it with minimum effort. If it is a bare .rb, the user has to deal with installing it manually.
About the same time, SketchUp added the idea of an "Extension", which is just a plugin with a particular structure that helps SketchUp to manage it. The base .rb file of an extension contains special code that registers the extension/plugin with SketchUp. This code both identifies the extension and tells SketchUp how to load the rest of it. This information allows SketchUp to decide whether or not to load the entire extension based on user settings. In recent releases they have also added "signing" by which it is possible to verify that an extension's contents have not been tampered with and also to set restrictions on what extensions can and cannot be loaded.
So, to reiterate, an extension is just a special kind of plugin. Today, because of their advantages, extensions are preferred over bare plugins. But there are still bare plugins available from various sources, particularly ones that the author is not actively supporting. And the two terms are often used loosely and interchangeably.
At some point (I don't remember exactly when) SketchUcation (one of the oldest and most reputable independent SketchUp sites) created their "Plugin Store". It is a repository in which almost anyone can place a plugin and it includes a very nice system to download, install, and manage all your extensions/plugins. There are literally thousands of plugins available from SketchUcation. Their manager is itself an extension that you download and install to start using the system. SketchUcation's store is user-supported; it relies on its members to discuss the merits or flaws of the plugins and to report bugs to the author.
Trimble's Extension Warehouse is conceptually similar to the SketchUcation plugin store, although Trimble reviews and approves all extensions before admitting them to the EW. This makes it somewhat less eclectic than SketchUcation's plugin store, but also perhaps a bit safer (not to suggest that SketchUcation's store is not safe!).