SIM Cards are using a Microprocessor or Microcontroller?
A SIM Card is closer to a microcontroller than a microprocessor as it has all the required logic blocks including memory etc.

It differs from a microcontroller because it is a dedicated application circuit specifically designed with the security implications in mind.  It is not a general purpose circuit like a microcontroller that can be used in many different types of applications (even if microcontrollers are more or less targeted to a field of applications).
A microcontroller can not provide the level of security that a SIM Card provides.