A button has not state, only events. So it cannot be a "condition" (what condition is it in just sitting there?). So a button can only be a trigger event. Trigger events can be used with Triggers, and with Triggered Rules. As Mike says above, most button-press-cause-action things can be done with Button Controller. Button Controller has most of the actions available in Rule Machine.
A rule has conditions. This implies they have a state that can be tested. For example, a switch is either on or off -- that's its state. Now, these sorts of devices also have events: turning the switch on is an event, one that changes its state. What a rule does is examine the conditions (states) whenever there is an event for one of them. There would be no point in examining them at any other point in time, because they would just be what they were the last time -- until there is an event. Only an event would change their state. So, we just look at all of them for every event for any of them. This is where the rule part comes in: what is the logical relationship between the various conditions that we want to see? For example, light is on and day is Tuesday.
Consider that one for a moment: We want to find out when that is true, and then do something. So, first of all we want to check every time the light turns on or off if it's Tuesday or not. If the light turns on and it is Tuesday, then our rule would be true, and we'd do whatever it is we want to have happen. But, how about the case where the light is left on Monday night. At midnight it becomes Tuesday. So, we have to check then to see if the rule is true also. Each condition (is it Tuesday, and is the switch on) has an event that happens and all of those events are important for the truth of the rule. The Tuesday event happens at midnight Monday night (it becomes true) and at midnight Tuesday night (it becomes false). The switch event happens every time the switch is turned on or off.