Quick answer: both correct and interchangeable. But...
Different sources will recommend one over the other
Which is more common is a good way to determine which is appropriate/proper. So which do people google more often? Advisor is 10 times more common according to Google Trends:
If you believe that democracy dictates words and language (if an "unofficial" or slang word is used enough, it's suddenly recognized as proper or official) then the more common "advisor" would be proper and "adviser" is ... something less. But there are other rules; lines drawn in the sand at something of a different angle surrounding you and making any choice arguably wrong. Consider:
Interchangeable / synonymous (hee hee) according to:
American Heritage Dictionary
Random House Unabridged Dictionary
Purdue Style Guide (a shorter discussion on their website) (because their teaching assistants are officially called advisors, never advisers):
The -or ending is the IPFW-preferred spelling over the -er ending (adviser). Note, however, that if an official name uses the -er spelling, such as a specific Board of Advisers, then it should be retained.Prefer Adviser:
Columbia Journalism Review
National Scholastic Press Association
An alternative view:
An advisor is expert, possibly professional. An adviser is someone giving out information, but not as an expert or based on something separate from his expertise.
The guy at the insurance office who is trying to sell you more coverage, not because you need it, because he gets a bigger bonus if you buy more may call himself an adviser - he's giving advise but it's not based on his expertise, it's based on his bottom line. A college department advisor may recommend job shadowing someone in your considered field because she knows that it's not for everyone based on her expertise and experience.
Many websites suggest which is the best credit card - say the best cash back credit card. They consider fees, the amount of the reward, the ease of interacting with the issuing company and it's representatives, when you get your rewards, and more.
But they also consider which credit cards offer "affiliate programs" ... in other words, which will send them a payment if someone clicks a link on their page then signs up for a new credit card.
You may get good advise from these folks, but it has a built in set of limitations and bias that is glossed over if disclosed at all. This is not the advise of a friend who's been through the same question/issue recently.
I hope I can act as an advisor on my friends and family (and whoever you are) in some decisions that have come up in my life only to be researched to death.
For better or worse, I spend too much time researching before making decisions ... about how to prepare for retirement, which books to buy, the best phone or carrier, which is the best type of sweptback handlebar for your touring/commuter bike, etc.
I will consolidate my research on a more specific website one day, but for now I want to direct users to my Unclezeb blog to posts with the maximizer tag:
Abe's research, reviews, and advise is here!