In general, adviser and advisor are interchangeable. However, adviser is used more generally to mean someone who is giving advice (what they are doing), whereas advisor is more commonly used when it means the primary role (what they are), such as job title, etc.
In the UK, Ireland, Australia and Asia the spelling is traditionally adviser, though US spelling advisor is becoming increasingly common. In the US, the Associated Press and New York Times style is adviser, and most newspapers and some magazines follow that spelling, while US federal government style, other government agencies, and many businesses prefer advisor. News organizations around the world may change spelling found in sources, even in quoted material. US book publishers may be less likely to change spelling in quoted material because the practice is contrary to The Chicago Manual of Style.