Adviser and advisor are both accepted spellings of the noun meaning one who advises or counsels. There is no difference between them. But adviser, the older version, is listed as the primary spelling in most dictionaries, and it is about five times as common as advisor in current news publications from throughout the English-speaking world.
In the U.S. and Canada, advisor is commonly used in official job titles, but adviser is still generally preferred over advisor in North America, and advisor is only marginally more common in American and Canadian English than in other varieties of English.
Most major publications, whether in the U.S., the U.K., or elsewhere in the English-speaking world, prefer adviser—for example:
A former campaign adviser to President Obama called on top administration officials to fire Energy Secretary Steven Chu. [USA Today]
Schools must do more to engage children who are passively “opting out” of lessons, the government’s adviser on behaviour has warned. [Guardian]
A senior nuclear adviser to the British government says Australia should consider enriching uranium. [Australian]
And advisor is sometimes part of an official title and sometimes just an alternative spelling of adviser—for example:
It is part of what provincial Early Learning Advisor Charles Pascal calls the “seamless day of learning.” [Toronto Star]
[H]e is not necessarily interested in a return to management and may prefer to work more permanently as an advisor. [Telegraph]