How do I use the global class \Drupal static methods to access services?
\Drupal::service('config.factory') and \Drupal::configFactory() are equivalent; the second is just shorter.

There are many, many services provided by core, and only a few of them have a dedicated method. You can get a list of core services on the core.services.yml page. Note that this is not all services that core offers, for example, there are more services in user.services.yml.

Also note that when working with classes, it's better to use dependency injection rather than calling static methods. Static methods should be called in procedural code (in D8, this basically means hooks, or API functions). 

This is a slideshow I used when doing a presentation on dependency injection at Drupal Camp Tokyo this month.