I very often get the question that what is the difference since both the microprocessor and microcontroller looks same.
One of the main difference between microprocessor and microcontroller (https://eeeproject.com/microprocessor-vs-microcontroller/) is that the microcontrollers are designed to perform a small set of specific functions, for example as in the case of a Digital Signal Processor which performs a small set of signal processing functions, whereas microprocessors tend to be designed to perform a wider set of general purpose functions.
For example, microcontrollers are widely used in modern cars where they will each perform a dedicated task, i.e. a microcontroller to regulate the brakes on all four wheels, or a microcontroller to regulate the car air conditioning, or a microcontroller responsible for the cruise control. These microcontrollers will perform few other tasks (if any) other than those specified. Compare this on the other hand to a microprocessor in a PC which performs a wide range of tasks related to the general requirements of a PC, i.e. performing the necessary calculations for a very wide set of software applications, peforming I/O for the main sub-systems, peripheral control etc.
I can't see the point of this distinction. This is the diagram from the OP's link
and it seems to me that an Arduino Uno has most of the elements of the right image. However on an Arduino almost all of that capability is inside the Atmega 328 microprocessor chip.
A microprocessor is a chip like the one that's (likely) in your computer or phone. Examples are the current Intel In series, the Motorola 68000 of the first Mac, or the Zylog Z80 used in the TRS80 and a kazillion other 8 bit hobbyist computers of the 1970s. Microprocessors need external circuitry for RAM, ROM, Flash, eeprom, etc. in order to function.
A microcontroller is like the ATMEGA328p on your Uno, , an ATTiny device or a PIC chip. It has all the memory it needs to function already built in to the same chip.
the microcontrollers are designed to perform a small set of specific functions ... whereas microprocessors tend to be designed to perform a wider set of general purpose functions.
This sounds more like the difference between an "embedded system" (dedicated function) vs a "general purpose computer." The controller/processor distinction is usually about the percentage of the functionality (CPU/RAM/ROM/IO) present in a single chip.