It's all a bit muddled, but I'll explain it the best I can.
At the moment, everyone has the entitlement to paid holiday of four weeks per year. There is no separate entitlement to paid bank holidays so, as you say, if you pay bank holidays you can count them against the four weeks.
From October, the entitlement for a full time employee will go up to 24 days and then, a year or so later, to 28 days. However, the rules on bank holidays are not changing at all. This means that, if you give bank holidays and pay them, they can count towards the 24/28 days.
This means that, in practice, the only people that the change will affect is those who currently pay 8 bank holidays and then only give 12 extra days' holiday per year. Because the total for that is only 20, those people will have to add on 4 more days to the paid holiday.
The reason that it gets all confused and people talk about bank holidays is that, once the law is brought in, the net result for most office based employees (who tend to get paid bank holiday as standard) will be that they will be granted four weeks paid holiday per year and will be paid for the 8 bank holidays. It does not mean that you can't set it up differently if you want to.