There is one Pound Sterling, which is represented by Bank of England, Scottish and Northern Irish notes and by Royal Mint coins (there aren't separate coins in England, Scotland and Northern Ireland).
Gibraltar, the Falkland Islands and Saint Helena (overseas territories) and Jersey, Guernsey and the Isle of Man (crown dependencies) each have their own pounds which are pegged at one-to-one with the pound sterling. They each issue their own notes (to their own designs) and coins (which have the same weights and compositions as Royal Mint coins but have different designs). In theory, they could be floated, in which case there would be an actual exchange rate; but the governments of those overseas territories and crown dependencies choose to maintain the peg at par.
Historically, the Republic of Ireland issued its own pound (or punt in Irish) and was maintained at par with sterling until 1979, when it was floated and there was an exchange rate until the Irish pound became part of the euro in 1999.
There is then the separate question of the acceptability of notes and coins. Legal tender is an irrelevance in a shop - it's always up to the shopkeeper what notes they will accept. It's only meaningful for settlement of a debt (e.g. in a restaurant or a taxi where the service has already been provided before payment) and even then, any note can be refused by any business other than a bank because they think it might be a forgery (banks will instead take and destroy the forgery). For that reason, many shops and other businesses will not accept notes that they are unfamiliar with, as they are concerned about forgeries and unable to tell genuine notes from forged ones. This doesn't just affect non-English notes in England and Wales (especially in smaller businesses and outside major cities), but also the Bank of England £50 note, which is not in wide circulation (few ATMs will issue £50s) and is often refused.
Scottish and Northern Irish notes are generally more likely to be accepted in England by larger businesses, in major cities and (for Scottish notes) close to the border - that is, in places where they are more likely to see them on a regular basis. For the more obscure notes, they are less likely to be accepted in businesses; you may have to take them to a bank to exchange for Bank of England notes. All banks are obliged to do this with Scottish and Northern Irish notes; they usually will in practice with crown dependency or overseas territory notes, but technically this is a foreign currency exchange for which they could charge. In practice, they don't.
Northern Irish notes are accepted more than they used to be; confusion with the Irish pound meant that many were concerned about accepting them and mistakenly taking a foreign currency that was worth slightly less than the pound sterling (like US and Canadian dollars). With Ireland switching to the Euro, this concern has faded.
CD and OT Coins, because they have the same weight and composition as Royal Mint coins, all work in vending machines. Cashiers in shops and other businesses often fail to notice that they aren't Royal Mint coins and will accept them as a result; some of them will accept them even when they know what they are, but most cashiers have been told not to, usually because there are lots of forged £1 coins in the UK and they are not trained to distinguish a non-Royal Mint coin from a forgery.