Back in the 15th Century, pepper was a highly regarded and relatively valuable spice. When the Spanish bumped into the Americas, they were so desperate to find rare, sought-after spices, and the poor dears had been at sea for so long, that when showed allspice berries by the natives they thought they were pepper!
The result was that Felipe IV of Spain instructed his minions to investigate la pimenta de Jamaica, ‘pimenta being Spanish for pepper. Imagine the red faces when ships laden with allspice berries landed in Spain, the traders expecting to see valuable black pepper instead!
Therefore, for many years allspice was called Pimento and/or Jamaica Pepper.
Pimento also refers to members of the chilli family, another naming by the Spanish explorers when they noticed chillies from the New World were hot like black pepper (Piper nigrum). That’s why members of the chilli family are called ‘peppers’ in many countries. When you see green olives stuffed with ‘red pimento’ the pimento reference is to capsicum/paprika.
In an attempt to avoid this pepper/pimento confusion the spice trade started calling these berries Allspice. The reason; the flavour is like a combination between cinnamon, cloves and nutmeg (all spices). In reality the flavour is most like a mild, somewhat fruity version of cloves.
Mixed spice is much milder than Allspice, and although they are used in similar recipes, we don’t consider them to be interchangeable.