Barbudo vs. barbado
The Spanish words barbudo and barbado both translate to bearded in English when referring to people. However, they possess subtle differences in nuance, and barbado also has broader applications beyond describing human facial hair.
Barbudo
A2Barbudo is an adjective that describes a person, typically a man, who has a beard. It often implies that the beard is prominent, abundant, thick, or a defining characteristic of the person. It can sometimes carry a more emphatic or descriptive weight than barbado.
El viejo marinero 'barbudo' nos contó historias de sus viajes por el mundo.
(The old bearded sailor told us stories of his travels around the world.)
Muchos filósofos de la antigüedad son representados como hombres 'barbudos' y sabios.
(Many ancient philosophers are depicted as bearded and wise men.)
Mi tío es el más 'barbudo' de la familia; su barba le llega hasta el pecho.
(My uncle is the most bearded in the family; his beard reaches his chest.)
En el bar entró un grupo de leñadores 'barbudos' y ruidosos.
(A group of bearded and noisy lumberjacks entered the bar.)
El personaje principal de la leyenda era un rey 'barbudo' y justo.
(The main character of the legend was a bearded and just king.)
Barbado
B2Barbado is an adjective that primarily means bearded or having a beard when referring to people. It can be a more neutral or general descriptor than barbudo. Importantly, barbado is also used to describe plants or animals that have barb-like appendages, bristles, or awns (like bearded wheat). It is also the past participle of the verb barbar (to grow a beard, or for something to develop barbs).
El testigo describió al sospechoso como un hombre 'barbado' de estatura media.
(The witness described the suspect as a bearded man of medium height.)
El 'trigo barbado' es una variedad que tiene aristas largas en sus espigas.
(Bearded wheat is a variety that has long awns on its spikes.)
Algunas especies de peces, como el pez gato, son 'barbadas' debido a los filamentos cerca de su boca.
(Some species of fish, like catfish, are bearded (have barbels) due to the filaments near their mouths.)
El actor apareció 'barbado' en la alfombra roja para promocionar su nueva película.
(The actor appeared bearded on the red carpet to promote his new movie.)
La flor del 'lirio barbado' tiene una distintiva 'barba' en sus pétalos inferiores.
(The flower of the bearded iris has a distinctive beard on its lower petals.)
Se dice que un coco está 'barbado' por las fibras que tiene.
(A coconut is said to be bearded because of the fibers it has.)
Summary
In essence, while both barbudo and barbado mean bearded when describing people, barbudo often suggests a more noticeable, significant, or characteristic beard. Barbado can be a more general term for a person with a beard and, crucially, is also used to describe plants and animals possessing barb-like features, bristles, or awns. While sometimes interchangeable for people, barbudo tends to emphasize the beard itself more strongly, whereas barbado can simply state the fact of having one or refer to its other botanical/zoological meanings.