The UK police didn’t shut down English Shooting, They yanked his firearms license because of some of the comments to his videos.
English Shooting shut down his channel voluntarily in order to get his firearms license back.
A difference without much of a distinction.
Without a firearms license, he could not do much of a firearms video.
This is how the nanny state operates. All of this “may issue” nonsense gives an enormous lever of control.
When something is a matter of subjective judgement to the powers that be, they use it to control all your behavior.
I have seen many examples of people curtailing what they legally can do, because of fear of what the powers that be can do to them with subjective judgements.
To my mind, the only distinction is that the UK police acted on what they control - his firearms license. The headline makes it sound as if the UK police went to YouTube and ordered them to take down the channel.
But you are right, of course, that the end result is the same.