Is there a difference in the meanings of "India Pale Ale" and "Indian Pale Ale"? I mean, without considering that "Indian Pale Ale" is an incorrect term for a sort of beer, would a native speaker have different conceptions/ideas for these two phrases?
The correct term is "India Pale Ale," so "Indian Pale Ale" would be wrong. However that said, someone already knowledgeable of what an IPA is would have no troubles understanding you, and someone unfamiliar with the term would still require explanation just the same.
So I don't believe the change would make too much of a difference in interpretation. Technically "Indian Pale Ale" could be interpretted as a pale ale from India, but again, this would likely only be the case of someone unfamiliar with the term.
India Pale Ale (note capitalisation) is a style of beer, originally brewed in 19th Century Britain for export to India. It was specially formulated to survive the long sea voyage. The style became popular in the home country and is now made all over the world. Without any additional information, "Indian Pale Ale" could simply mean "pale ale from India", or it could be an error for "India Pale Ale", in fact the capitalisation suggests this.