Regular stop is normal procedure as stated above. It allows (like a start) to operate machine.
Emergency stop bears defensive role - it should protect people from injury and equipment from breaking. In my practice E stop can be done with PLC. The reason is - E stop is also a sequence of actions. Generally you can't cut off power supply of all actuators and say "Now it's safe". What you really need - stop safely as fast as possible. But safety is priority. E stops can be also divided into classes - "clean" allows you to stop without any damage, but if this one is not fast enough you may bump into more strict defense sequence, thus decreasing stop time, but allow some equipment damage.
Overall E.Stop should provide minimum damage (not necessary no damage). Sequence should be provided by machine manufacturer and industry standards (which are different in different countries).