Tapa vs. tapadera
Both tapa and tapadera translate to lid in English and are used to refer to the cover of a cooking pot or pan. While they are often used interchangeably in the kitchen, tapa is a more general and widely used term for any type of cover, whereas tapadera specifically refers to a removable lid used for pots, pans, or containers, and sometimes carries a more traditional or regional feel.
Tapa
The word tapa is the most common and versatile term for any kind of lid, cover, or top. In the kitchen, it refers directly to the lid of a pot or pan, but its usage extends to jars, boxes, bottles, and even book covers.
No encuentro la tapa de esta olla a presion por ninguna parte.
(I cannot find the lid for this pressure cooker anywhere.)
Levanta la tapa con cuidado para ver si el agua ya esta hirviendo.
(Lift the lid carefully to see if the water is already boiling.)
Esta sarten nueva viene con una tapa de cristal templado.
(This new pan comes with a tempered glass lid.)
El guiso tradicional debe cocinarse a fuego lento y sin tapa.
(The traditional stew should be cooked over low heat and without a lid.)
Coloca la tapa sobre la cazuela para conservar el calor antes de servir.
(Place the lid on the casserole to keep the heat in before serving.)
Tapadera
The word tapadera is a more specific term that strictly refers to a removable lid used to cover pots, pans, and containers. While it means the exact same thing as tapa when cooking, it is sometimes used to emphasize the physical object made expressly for covering a vessel, and it can be more common in rural areas or specific regional dialects.
Mi abuela siempre usa una vieja tapadera de aluminio para hacer el arroz.
(My grandmother always uses an old aluminum lid to make the rice.)
El vapor era tan fuerte que empujaba la tapadera de la olla hacia arriba.
(The steam was so strong that it was pushing the lid of the pot upwards.)
Compramos un juego completo de ollas pero nos dimos cuenta de que le falta una tapadera.
(We bought a complete cookware set but realized it is missing one lid.)
Pon la tapadera en la sarten para que el aceite caliente no salpique tu ropa.
(Put the lid on the pan so the hot oil does not splash your clothes.)
Se me cayo la tapadera de barro al suelo y se rompio en mil pedazos.
(I dropped the clay lid on the floor and it broke into a thousand pieces.)
Summary
In short, tapa is the everyday, universal word for any lid or cover, including those used for pots and pans. On the other hand, tapadera is a slightly more specific or traditional word that refers expressly to the removable lid of a cooking vessel or container. Both words are perfectly correct when referring to cookware, but tapa is much more frequent in modern, daily speech.