Difference between "instantly" and "instantaneously"

Is there a case in which "instantaneously" can be used in which "instantly" cannot? If not, why does the former exist? If so, what are the circumstances dictating that usage?

Solution 1:

According to this post on the Grammarist, there is a difference between the two. They write:

Instantly means at once or immediately. Instantaneously means happening so soon (in relation to something else) that no delay is perceptible. The difference between these adverbs is subtle, and there is plenty of gray area between them, but careful writers keep them separate.

Instantly is synonymous with immediately, but instantaneously is closer to with little delay. They give the following examples of each:

I don’t use Twitter often, but I like how my Tweets appear instantly on my Facebook page. Buzz delays them for hours. [Boston Globe]

Mr. Lingamfelter argues that advances in technology mean that gun sellers can now verify that buyers are not felons instantaneously through the National Instant Check System . . . [Washington Post]

So, yes: there are cases when one should use instantly instead of instantaneously and vice versa. They represent two different ideas about when something happens. However, despite the fact that one could distinguish between them, one does not necessarily need to in practice:

But while drawing this distinction between instantly and instantaneously is nice, in practical usage the words are usually used interchangeably.