Although similar, the facial expresions are iterpreted differently, what Trope
FatGiant a few other users from here sharing "hispanic - romanic culture " call sad smile, Can be read in the Germanic - Angloamerican Culture as "pittyfull smile"
I persnally have my fun, with the 28 jhr old son of my better Half, and he with me missreading our facial expressions, (he was near 2 when he got to the US and he grew up there) they are similar but often have a different meaning.
"sonrisa triste", y would translate as sad smile and into german as trauriges lächeln, or gequältes lächeln (for the last you could say tortured or painfull smile)
There is a saying from the Argentinan Poet Almafuerte,: Smile because it is better to have a sad smile in life, as the sadness of a life without smile ( Sonrie, mas vale tener una sonrisa triste en la vida, que la tristeza de una vida sin sonrisa