The most common expression is prendre en photo which is equivalent to photographier. Here one or more photos are taken and the focus is made on what is shot.

“Prendre une photo” is more common than “faire une photo.” Unlike with “photographier/prendre en photo” only one picture is taken. With prendre une, the focus is on the shooting while with faire une the focus is more on the result, a picture. That’s likely the reason why it looks more suitable for photographers where post processing and professional printing is part of the process.

In most cases though, both forms are interchangeable.

i would use “faire une photo” if i was doing something in photoshop and “prendre une photo” if some tourist wanted me to take a photo of them.