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.
Note how in these examples, instantly is synonymous with immediately:
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]
Some of the marquee Olympic events are tape-delayed this month, even though Olympic results are instantly available on the Web. [NY Times]
And note how in these examples, instantaneously means with little delay rather than immediately:
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]
The problem is that the raunchy trailers pop up on sites without age restrictions almost instantaneously. [NY Times]
But while drawing this distinction between instantly and instantaneously is nice, in practical usage the words are usually used interchangeably.
