According to Wikipedia a microcontroller is a small computer on single VLSI integrated circuit (IC) chip. It contains a one ore more CPUs (processor cores) along with memory and programmable input/output peripherals. Microcontrollers are used in automatically controlled products and devices. A microprocessor consists only of CPUs (central processing units).
The top 10 popular microcontrollers among ‘makers’ (a person or thing that makes or produces something) is listed and described here. The second most popular microcontroller is the ATmega328 created by Atmel and at retail costs less than $3.00. The microcontroller chip is used in many projects and autonomous systems where a simple, low-powered, low-cost microcontroller is needed. This microcontroller is an integral part of the Adruino development platform which includes the Arduino Uno which is used in a number of robot STEM kits.
Arduino is an open-source hardware and software company, project and user community that designs and manufactures single-board microcontrollers and microcontroller kist for building a variety of different digital devices. Adruino microcontroller boards support several different CPUs (Atmel 8-bit and ARM Cortex 32 bit), and are programmed a simplified C++ variant.
If you are scratch building a robot, typically you will define and purchase a controller board that is Arduino based. But, which board? Here is a description of the various boards that you might consider, or may have been included in a kit that you have purchased.