The names get confusing!
Bell peppers or sweet peppers (capsicum) come in red, yellow and green varieties. The colour just tells you how ripe it is, they are the same thing!
They are related to potato, tomato, aubergine, latex (the nightshade family). You are not automatically allergic to all of these things, but you may have a higher risk if you are already allergic to one or more of them.
Chilli peppers are closely related to bell pepper. There are lots of different ones, both red and green eg bird’s eye, Scotch bonnet, jalapeno, chipotle.
Chilli powder, paprika, cayenne, pimento are all spices made from these plants, so if you are allergic to the vegetable there’s a good chance you will react to these spices too. These get used to make pepperoni, salami, chorizo sausage and others.
Black and white pepper are completely unrelated! You do not need to avoid these.
Cross contamination can be a big problem, since in restaurants, the same knife and chopping board will get used for chopping bell peppers and all other vegetables. Chargrilled food is also a risk if cooked on the same surface as roast peppers! Ask restaurants to use separate knives, chopping boards, frying pan etc.
Ketchup, baked beans, BBQ sauce, crisp flavourings, stock cubes, soups are all potentially a problem, as are most ready meals, you will need to look closely at the ingredients label.
Paprika extract is used as red/orange colouring in lots of things.
You might need to avoid anything with unidentified ‘spices’ or ‘flavourings’ until you can get further details from the manufacturer.
You may not react if the amount of spice used is very low, but this is hard to predict and you may find that one time you don’t react but another time you do react to the very same thing.
Abroad, food can be very different and you need to be much more careful. In Serbia and Croatia, for instance, there is a traditional tomato sauce ajvar that often gets served on the side of meals, which is made with red peppers.
(With thanks to Julia Marriott)