Papa vs. patata

Both 'papa' and 'patata' are Spanish words for the English term 'potato', but they are used differently based on geographic distinctions in the Spanish-speaking world.

Papa

This word is most commonly used in Latin America and parts of Spain to refer to a potato.
Me gusta comer papas fritas.
(I like eating French fries.)
La sopa de papa es muy popular en Perú.
(Potato soup is very popular in Peru.)
Las papas son un alimento básico en muchos países latinoamericanos.
(Potatoes are a staple food in many Latin American countries.)

Patata

This word is typically used in Spain to refer to a potato.
Las patatas bravas son un plato típico español.
(Patatas bravas are a typical Spanish dish.)
Voy a hacer una tortilla de patatas para la cena.
(I'm going to make a potato omelette for dinner.)
Puedes pelar las patatas, por favor?
(Can you peel the potatoes, please?)

Summary

'Papa' and 'patata' both mean 'potato' in Spanish, but they are regionally specific. 'Papa' is more commonly used in Latin America and parts of Spain, while 'patata' is primarily used in Spain.