The English "to be true" can be translated to Spanish as either ser cierto or ser verdad. What is the difference between the two? When would you use one instead of the other?
you should think as 'cierto' = right / correct and 'verdad' = true.
'cierto' it's normally used as "es cierto" which means "that's right." while "verdad", normally used as "es verdad" means "that's true.'
ser cierto / ser verdad, even it can be ok depending the sentence, it's not used quite often.
In practice, they can be used almost interchangeably. Just make sure the syntax is correct for the type of word you're using ;)
Es cierto // Es la verdad // Es verdad
Lo cierto es que... // La verdad es que...
Es cierto lo que dices // Es verdad lo que dices...
However, some constructs will only appear one way:
Dime la verdad.
cierto is basically identical to
It's weird to read those literal translation. "To be true" will never be expressed as "Ser cierto" or "Ser verdad".
Aside for their differences, as mentioned here —'cierto' being an adjective and 'verdad' a noun—, you would never read "ser cierto" in its infinitive way, only with the ser (to be) verb conjugated You will find that something either is or not true ("es o no cierto"), or some things ("son o no ciertas")
Likewise, "ser verdad" sounds odd, as you would never hear or read those two words put together. You could find that something "es verdad" o "es la verdad" (ie: "es verdad que tuve miedo, era la primera vez que hablaba ante una multitud" ['it's true that I was scared, it was the first time I spoke in front of a crowd']
Though 'verdad' as a noun is commonly spoken or written in the way 'truth' is used ("la verdad es que la noticia me hizo más feliz de lo que esperaba" ["it's true that I was scared, it was the first time I spoke in front of a crowd_"]), "cierto and verdad" also act as synonimous:
¿es cierto que vas a mudarte a otra casa? [is it true that you are moving to another house?]
¿es verdad que vas a mudarte a otra casa? [same meaning]
Strictly speaking, there is a difference: "es cierto" means that something is manifestly true, with certitude.
In current common use, however, there are equivalent: "es verdad = es cierto = it's true".