The x86 is developed based on the Intel 8086 microprocessor and its 8088 variant where it started out as a 16-bit instruction set for 16-bit processors where many additions and extensions have been added to the x86 where it grew to 32-bit instruction sets over the years with almost entirely...
Commonly, an SoC can be based around either a microcontroller (includes CPU, RAM, ROM, and other peripherals) or a microprocessor (includes only a CPU). It is also possible for SoCs to be customized for a specific application, including whatever components, memory, or peripherals necessary, ...