I am a bit late to the discussion. I think these paragraphs from this solicitors' website explains it concisely.
https://www.howatavraamsolicitors.co.uk/selling-goods-online-when-do-you-become-legally-bound-to-deliver/#:~:text=By%20placing%20an%20item%20in,confirms%20receipt%20of%20the%20consideration.
"Displaying items for sale on a website does not constitute an ‘offer’ under UK law. Instead, it is an invitation for third parties to make an offer to buy. By placing an item in a shopping basket online, a consumer is making an offer to buy those items at the price and on the terms listed on the website. However, a binding contract will only be formed online when the supplier accepts an order and confirms receipt of the consideration."
"To avoid customers insisting that goods are sold at the price listed on a website, many businesses delay their acceptance of the customer’s ‘offer’ by first issuing an order acknowledgement. This enables the supplier to decline a customer’s offer if it transpires that there are errors on the website or that the item is no longer available. If a confirmation or acceptance is automatically issued on receipt of an order, a binding contract has been formed and the supplier will be in breach of contract if they fail to deliver on the terms originally listed. In order to avoid allegations from consumers that they have been misled, the supplier’s standard terms of business should set out the contractual process and make clear at what point the legally binding contract will be formed."
Hence there is definitely no contract in scenario B in my view. The displayed price is only in "invitation to treat". You are making an offer and the seller has the right to reject the offer.
In scenario A, I think it is invariably the case these days that you get an "order acknowledgement" when you have given your card details to buy something. Then you get a confirmation of the order at a later time (usually within 24 hours). The T&C would very likely also confirm that there is no contract until the order is confirmed.
Personally, I don't feel comfortable with buying something that has obviously priced wrongly. E.g. something worth £3000 priced at £30.00. However, I do agree that not "updating" your price on your website is extremely poor on the seller's part.
(Incidentally, I once saw a real leather briefcase at Debenhams with an original price of something like £150. Then it was reduced to "£5" after Christmas. I said to a sales assistant that surely the price cannot be correct but she said it was. I went ahead and brought it even though I didn't need the case.)