Palmera vs. palma
While the Spanish words palma and palmera share the same etymological origin, they usually refer to distinct physical concepts. Generally, palmera is the tree itself, while palma refers to a part of the human body or a specific part of the plant.
Palmera
A2This word refers specifically to the palm tree as a whole biological plant. If you are describing the trunk, leaves, and fruit (like coconuts or dates) in a landscape, usage of palmera is the most accurate choice.
La palmera más alta del jardín se rompió durante la tormenta.
(The tallest palm tree in the garden broke during the storm.)
Esa región es famosa por su producción de dátiles de palmera.
(That region is famous for its production of palm tree dates.)
El hombre trepó la palmera para bajar unos cocos.
(The man climbed the palm tree to get some coconuts down.)
Me encanta el sonido del viento moviendo las hojas de la palmera.
(I love the sound of the wind moving the palm tree leaves.)
Palma
B1This word usually refers to the anatomical palm of the hand. However, it can also refer to a single palm leaf (frond), particularly in religious contexts (Palm Sunday), or acts of clapping (applause). In some regions, palma is used to mean the tree, but palmera is the standard word for the plant regarding botany.
Tengo una cicatriz en la palma de la mano derecha.
(I have a scar on the palm of my right hand.)
La gente agitaba una palma mientras comenzaba la procesión.
(People waved a palm branch as the procession began.)
El sudor hacía que la moneda se resbalara de su palma.
(Sweat made the coin slip from his palm.)
Todos tocaron las palmas al ritmo de la música flamenca.
(Everyone clapped their hands to the rhythm of the flamenco music.)
Summary
To distinguish them easily, use palmera when talking about the tropical tree found on a beach. Use palma when referring to the inner surface of your hand or a single leaf used for decoration.