Jamaica pepper /allspice: pimienta de Jamaica
The name "allspice" was coined as early as 1621 by the English, who thought it combined the flavour of cinnamon, nutmeg and cloves.
bell pepper: morrón.
There are many colour varieties: red pepper, yellow and green pepper.
black pepper: pimienta negra
It is usually dried and used as a spice and seasoning.
Apart from having a cuisine use, it has a medical usage: capsicum is an excellent source of laxative (purgative) and pain relief.
chili pepper: pimiento chile (muy picante)
Christopher Columbus was one of the first Europeans to encounter them (in the Caribbean), and called them "peppers" because they, like black and white pepper known in Europe, have a spicy hot taste unlike other foodstuffs.
chili powder: ají molido
It is used in many different cuisines, including Indian, Tex-Mex, Chinese and Thai.
hot sauce, chili sauce or pepper sauce: salsa picante.
It refers to any spicy sauce made from chili.
Paprika is a spice used in many cuisines to add colour and flavour to dishes.
white pepper: pimienta blanca
White pepper is sometimes used in dishes like light-coloured sauces or mashed potatoes, where ground black pepper would visibly stand out.