They typically mean the same thing, but "ghost" is way more common. "Apparition" can also mean a ghostly sight. You might see "apparition" in advanced literature.

They can often be used interchangeably but an apparition can refer to any type of vision which appears. If someone says " An apparition appeared before me" they could be referring to a ghostly apparition or simply a person whos appearance is remarkable for some reason. Which it is, will be defined by context.