I ran across two sentences: Марина вышла замуж за Павла and then Марина замужем недавно. What is the difference between using вышла замуж as opposed to замужем? Are they basically synonyms or are there specific contexts in which one is used over the other?
выйти замуж is 'to marry (about women)', and
быть замужем is 'to be married (about women).'
"Марина вышла замуж за Павла." means 'Marina [has] married Pavel.'
This sentence tells us that Marina is (or was) married, and her husband is (or was) Pavel. Note, this sentence is in the past tense, it tells about the fact of Marina's marriage and about her husband, but it gives no information as for whether she is still married.
"Марина замужем недавно." means 'Marina has been married recently.'
This sentence tells us that Marina is married now, and it also tells about how long ago the marriage happened. This sentence is in the present tense. You can also specify the name of the husband in this sentence, like this:
"Марина замужем за Павлом недавно." means 'Marina has been married to Pavel recently.'
Also note, that in the first sentence it is
за + Accusative case, but in the second one it is
за + Instrumental case.