Passing rules

Is "rule pausing" from within another rule the same as ticking the box next to the rule in the UI?

Sort of, but not really. Pause can be done as an action of another rule, but does not disable the rule.

Ticking the box disables the rule (or any app) and it cannot be viewed or edited when disabled. The intention behind disabling is primarily troubleshooting.

What is does is to disable the rule the same way that a Restriction would. You can also pause a rule from its UI. This does the same thing as pushing that UI button. It's the simplest way to disable a rule from another rule.