What are the three types of GFCI?

Could you elaborate on the three distinct types of Ground Fault Circuit Interrupters (GFCIs) that are commonly found in electrical systems? I'm particularly interested in understanding the differences in their functionality, installation requirements, and the environments where they are typically utilized. Are there any specific safety considerations that need to be taken into account when dealing with each type? Additionally, could you provide a brief overview of the advantages and disadvantages of each GFCI type to assist in making an informed decision regarding their usage? Your insight into this matter would be greatly appreciated.