"Pence" is an amount of money. A "penny" can mean the coin whose value is one pence, or it can be another way of saying "pence." In the old days--before the UK decimalized the currency--there was a coin called a "tuppence" whose value was 2 pence. If I said "I need two pence," you could give me either two pennies or one tuppence. But if I said "I need two pennies," a tuppence would not do.

No difference between one pence (or 1p) and one penny. “A” pence isn’t used.