In my experience, delusions in a mental health way would be ones that directly affect you and are distressing or exhilarating.

For example:
if you thought your neighbor was trying to harm you in your sleep.
if you thought people wearing sunglasses were government spies.
if you thought a bird perched on a tree outside was a sign of the heavens that you were the new jesus
if you thought a newscaster was sending messages to you to declare their love through a tv

These things are personally affecting you that invoke a reaction. Believing someone famous is alive or dead when they aren't is more of an odd quirk that some people might believe or not. However, sometimes these odd conspiracy ideas are a warning sign that a delusion will develop. Like you may start out thinking a famous person is alive that isn't and then it morphs into you thinking they are trying to contact you somehow.