Cara vs. rostro
While both 'cara' and 'rostro' can be used to refer to a person's face in Spanish, there are subtle differences in their usages and connotations, often influenced by regional language usage.
Cara
face (often referring to the front part of the head, including eyes, nose, mouth, forehead, cheeks and chin)
Lavate la cara antes de cenar.
(Wash your face before dinner.)
Su cara se puso roja de vergüenza.
(His face turned red with embarrassment.)
No puedo olvidar la cara de felicidad de María cuando recibió la noticia.
(I can't forget Maria's happy face when she received the news.)
Rostro
face (typically used in more formal or literary context. May sometimes refer more specifically to facial features or expressions)
El artista capturó el rostro de la modelo perfectamente en su pintura.
(The artist captured the model's face perfectly in his painting.)
El rostro sereno del monje transmitía paz.
(The monk's serene face conveyed peace.)
En su rostro se reflejaba su angustia.
(Her anguish was reflected on her face.)
Summary
So though 'cara' and 'rostro' both refer to a person's face, 'cara' is used more commonly in everyday language and often points to the front part of the head. 'Rostro', on the other hand, may have a slightly more formal or literary tone or context, often intrinsically referring to more specific facial expressions or features.