Yes, if you are recording CCTV then you should:
- make sure everyone knows that they are being recorded.
- Only use the recording for the intended purpose
Both of those I'd assume the shopkeeper was complying with.
However under GDPR the footage should only be shown to someone with "legitimate interest". And a random teacher to identify them would not count. If you do show footage to anyone else then any identifiable person should be blurred out.
And you are right, FB CCTV/Ring doorbell posts would strictly speaking fall foul of GDPR in exactly the same way.
But you can see how it could be problematic.
Shopkeeper shows it to OP. OP says she has identified little Jonny in 8A. She tells the safeguarding person that Jonny has been shoplifting, and maybe she mentions it to the form teacher too.
Teacher pulls Jonny aside to ask a few questions... The door is open (as it should be for safeguarding if they're alone) and the rumours start that Jonny was shoplifting.
Only thing it wasn't Jonny. It was Milo in 7F who has a similar coat, but the Op doesn't teach them so isn't on their radar.
Yes, I have every sympathy with the shopkeeper, but he could fall foul of GDPR in this case.
I have limited sympathy with a lot of the FB recordings, as a fair number I've seen are either making assumptions ("This person walked up our drive and down again, and up the next one too. Watch out he's clearly trying to break in." <person three doors down> "sorry, mate, that's my brother. He was looking for my house and got lost"> or have missed out part of the recording to show what they want to see (such as the one I saw a couple of days ago which didn't show the person leaving the parcel on the doorstep - neighbours pointed that out)