To use vs Make use of. when to use what

When someone "makes use of something," it implies greater effort and significance than if that person just "uses" something.

Consider "Andrew uses his old telephone" versus "Andrew makes use of his old telephone." In the first example, there doesn't seem to be anything special about the way that Andrew is using the telephone, or the fact that it's old. A reader might be more interested in who he is calling, what he wants to talk about, and other such questions that don't have much to do with the telephone itself or the specifics of how or why Andrew is using it. The full sentence might end up being something like "Andrew uses his old telephone to call his old doctor."

But in the second example, it is clear that there is something more interesting going on. Perhaps it is important that it is an old telephone, and Andrew is some sort of tinkerer who has found some use for what most would consider an obsolete piece of technology. Or maybe Andrew is an interior designer and is creatively using parts of an old telephone of his as decorative elements in a client's home. The full sentence in this case might be something like "Andrew makes use of his old telephone to tune into an emergency radio band and send an SOS signal from the deserted island."

Ultimately, I feel, it's just a matter of how much you want to draw the reader's attention to the object that is being used or made use of and/or the person who is using or making use of the item.

To me the idiom is about usefulness.

You can use a telephone to make a call to anyone.

You can make use of the telephone to reach out to someone.

It enhances the usefulness of the tool you "are making use of"