Easiest way to describe the difference is this: Ride stops are designed to put the ride back in the "home" position and allow passengers to disembark without any other issues. These are used mostly for unruly guests, or in some instances when a certain set of parameters are met in the ride computer. Power is kept onto the ride during a ride stop. Emergency stops are used when a certain set of parameters within the ride computer is met, and the safety of those aboard might be threatened. Also, the operator has an E-stop button available for parameters not set by the computer (someone jumping over the fences and entering lockout for example.)
Almost all the rides at KI must be reinspected by maintenance after every E-stop situation, no matter if it is accidental or not. The reason for this is an E-stop is very harsh on the electrical systems of the newer style of rides, and maintenance wants to ensure that an accidental E-stop will not cascade into a bigger issue, or whatever caused the E-stop is fixed and did not trigger other issues with the ride. Most of these are 5 minute restarts (goes in, checks the ride computer, checks the circuit breakers, buttons it up, puts it to manual.) The only rides that I can think of off hand that do not have a hard maintenance reset are mostly "carnival" style rides that are up at the park, mainly due to the fact that for safety reasons, the E-stop is engaged in order to load and unload guests. The one that springs to my mind immediately is Kiddie Carousel. On that attraction, for safety reasons, the E-stop is pressed in after the ride cycle is done, and for further safety measures, the key is also removed until the ride cycle is ready to go.