Shallow DOF and blurred backgrounds are related, but they are not the same thing.
For example, if you shoot with the same subject framing and aperture using different focal lengths, then the DOF will be the same but the background blur will be different. Perhaps an example description with some pictures:
First shot is 50mm, f/1.2. The second shot is from four times further away, 200mm and f/2.8. Aside from the perspective difference, the key observations here are that the second shot has both more DOF and more blur.
So if you want more blur, you need to shoot from further back using a longer lens.
If you want less DOF, you need a faster maximum aperture at whatever focal length you use.
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