The difference between an Arduino development board and a microcontroller chip is that the development board contains almost every essential part needed to start a project on the board itself. It has a microcontroller chip and ports for connection or extension (refer Fig. 1). You can program the chip with inbuilt examples available on Arduino IDE (software) and observe the output right on the board, or by interfacing with external circuits.
On the other hand, for a single microcontroller chip (such as Atmega328 microcontroller as shown in Fig. 2), you need a lot of things. First, you need to buy a separate programmer board to program the chip. For building a project or experimentation with the chip, you need a breadboard or veroboard for circuit wiring/connections with other components, a DC power supply for the project, jumper wires, etc. You also need to search for program examples from various sources, books, and the Internet.
To work with Arduino, you need to work with the Arduino software programming language.