What is the similarity between refraction and diffraction?

The similarity between refraction and diffraction is that both of these phenomena involve the ability of a wave to change the direction of its propagation. In case of refraction, a wave changes direction as it crosses the boundary between two media. The diffraction is defined as "bending" of a wave around an obstacle that blocks its path of propagation.
Waves of any nature—mechanical, such as waves on the water surface, or electromagnetic, such as light—can undergo both refraction and diffraction.
One can observe refraction by putting a straw or a pencil in a glass half-filled with water. If one looks at the straw through a side of the glass, it will appear broken at the surface of the water. This is because the light changes direction as it enters the water from the air and vice versa.
A rainbow is another natural example of refraction of visible light. When light enters and exits water droplets in the air, the light waves of different frequency (different colors) come out at different angles with the original direction. Therefore, observers on the ground see the light separated into a spectrum of several colors.
The diffraction of light is hard to observe in everyday life because the visible light has a very short wavelength (400 to 700 nanometers). However, we often experience the diffraction of sound—a mechanical wave, created by variations in air pressure. We can hear someone speaking from around the corner because sound can bend around the wall, which functions as the barrier to its propagation. We can also observe how the waves created on the surface of a pond or a lake diffract around the rocks or other objects in the water.
Please see attached reference link for the further discussion and illustration of refraction and diffraction.
https://www.physicsclassroom.com/class/waves/Lesson-3/Reflection,-Refraction,-and-Diffraction