In an IoT application we have many choices. A broad range of microcontrollers is available right now as a chip and used as such. It is off-the-shelf. But it can also be part of a digital design, a system on chip with embedded software (firmware). Hence if the application requires a microcontroller, you could use a controller chip and some discrete components. If the controller needs hardware accelleration, additional (communication) interfaces, … then an application specific design is possible. Then you can implement what you want. Protoyping and low volume products can use an off-the-shelf solution, an FPGA. It is reconfigurable many times. So, if the volume is high enough, an ASIC is a possibility. Because, an ASIC is expensive to develop. Therefore, it is only interesting financially to spread this cost over a few million products sold. The business case (cost, budget, profit) will define the choice for the IoT application hardware.
My Quora space : HW accelerators eating AI
Interesting read as well: Is the raspberry pi a good platform for production IoT devices?