What is the difference between the adjectives "разный" and "различный". Are they used in different situations?
These are synonyms, and are interchangeable in many situations. Разный is more like different, whereas различный is more like various. When you're contrasting two objects, разный is preferable. For example:
У нас с сестрой глаза разного цвета (My sister and I have different eye colors)
У нас с сестрой глаза различного цвета( My sister and I have various eye colors)
The best way to find the difference is to try to replace them with each other in different contexts and see what happens ;-)
У нас разные мнения- our views are different but most likely they do not contradict
У нас различные мнения- our views very likely contradict each other
Занят разными/различными делами
два различных предмета- from an example here, you can see the opposition more clearly when 2 is used
So my conclusion is that these are synonyms but you should consider
различный if you want to underline the opposition / contrast / contradiction / conflict of some qualities or features.
различный as of a word in the same semantic field as the words:
различаться, различие. In Enlish it is differ, different, difference while
разный is more like various, not similar but can also mean different because
разный has a wider semantic field and is a more frequent word.