Merriam-Webster:

"[T]here are some cases in which one tends to be used more often than the other. Some people feel that 'advisor' is more formal, and it tends to be found more often when applied to official positions, such as an advisor to a president. When referring to someone who is serving in a military role, especially when using the term as a euphemism (as when claiming that troops are actually military 'advisers'), then 'adviser' is somewhat more common."

Makes sense. Not.

In my brain, an "adviser" simply advises, but an "advisor" occupies a paid position to do so.