Well, the difference between the BS EN & the EN is irrelevant really.
Remember there is no requirement to do anything to standards, as long as you can prove that what you are doing is just as safe.
To have a presumption of conformity, then one requires compliance with the harmonised standards as published in the official journal of the EU.
You won’t find any BS standards listed there.
As per the construction products directive harmonised standards as published in the official journal here:
Nothing else counts.
https://ec.europa.eu/growth/single-market/european-standards/harmonised-standards/construction-products_en
If you scroll down the list you will see that the BS standard is NOT listed only the EN standard.
It is the EN standard that you must quote on your DoC to comply with the CE marking directive.
The BS, DIN, etc. standards are not recognised.
Whether they are different or not makes no difference.
I would actually say that BSI page is not 100% correct, as it contradicts itself, because the standard that they quote at one point, is not listed in the official journal of the EU, the standard they state is based on the EN standard, but is not the EN standard.
They do also however, state the correct standard also.
So, the requirement under the Construction Products Directive is to CE mark to EN 1090 as amended.
NOT to BS EN 1090 as amended.
Subtle difference, but, it is a specific difference, that could result in illegal CE marking and an invalid DoC.