Let me start by saying I don't think the movie is "The Uninvited" with Ray Milland as I"ve read this movie's synopsis and the ending doesn't seem to match...

When I was young I remember seeing a black-and-white movie about a ghost haunting a house on a cliff. It was a murder mystery. The setting was very much like "The Uninvited," however, a man dies in the end by falling out of a high window onto the rocky shore below. A comment was made by people in the room that the dead man must have seen the ghost and thought it was ____ (whomever) and when he rushed to it he fell out the window. The ghost was a swirling smoke (as in "Uninvited") and with his death the mystery is solved.

I know this isn't much to go on, but it's been bugging me for over 40 years. Please help!

It sounds a little like the synopsis of "The Ghost and Mrs. Muir," which the
Database says was from 1947. Don't know if it is or not; you can read the
Plot summary at this link: The Ghost and Mrs. Muir (1947) - Synopsis