They are not differentiated as being formal vs. conversational. In fact, if I were to judge, they are both informal and would rarely be used in a technical/scientific paper. For example, you could write, "The car is really small" and "The car is very small". Both sentences mean the same thing - there is no nuance in meaning. But why not enrich your vocabulary by using words like "extremely" or "incredibly".
Let's get down to business.
REALLY: An adverb, which means that it's used to describe adjectives, verbs, or other adverbs.
VERY: An adverb, but with one hitch - it cannot modify verbs.
I really like it. (correct)
I very like it. (wrong)
But then it gets extra complicated because Very can modify the appearance of verbs in the past participle form, but only because these have been established as adjectives.
I'm a very driven person.
Driven, although the past participle of Drive, is actually supporting the adjective role in this sentence, describing the kind of person I am.
Really and Very can be interchangeable when they both modify an adjective.
She is a really interesting girl.
She is a very interesting girl.
However, there are times when they cannot be replaced by the other. Like I said before, Very cannot modify verbs.
I really think she is an interesting girl. (correct)
I very think she is an interesting girl. (wrong)
One more difference:
Really can also be used as an interjection - to show surprise or exasperation.
Me: I saw the band Twisted Sister last month.
You: Wow, really?
This was a question asked by one of the readers of this blog. If you have a question or suggestion for a blog post, feel free to contact me.