Refocus Examples
1)The base image was genereated in Hunyuan Image 3 (NF4)  It has a soft blur to the background that looks pretty natural - maybe a small format camera or f/8
2)The deblur image has essentially refocused the background to extend the DOF from foreground to infinity.  Note that the foreground and subject are also sharpened.
3)The refocus 1 image shows how refocus can further blur the background and make the subject stand out in the image a bit more.  You can play with the settings for blur and CoC to completely blur everything but the subject.  It was generated by making a small circle mask mark on the woman's face.
4)The subject is blurred and the background is deblurred in this Refocus example where I put a dark  mask spot on the input image near the 2nd car.

Deblur generally sharpens the background and foreground to make everything in the image in focus
Refocus resets the DOF to a point you select in the image by putting a mask spot on the input image or setting the refocus location with [x,y] percentage. 
Max_CoC and blur_strength settings in the Compute Defocus node will set how much to blur the areas outside the DOF. 