There are two main differences that I know of:
1)
"To marry" is transitive-- it requires a direct object.
Example: "Camilo is going to marry Sarah." (In modern, idiomatic English you cannot say "Camilo is going to marry.")
"To get married" is instransitive.
Examples: "Camilo is getting married." (You can still include information about his fiancée in a prepositional phrase beginning with "to": "Camilo is getting married to Sarah.")
2) While "to marry" most commonly means "to become a husband or wife," it can also mean "to preside over a wedding." That is, the rabbi, priest, ordained minister, or legal official can also be said to "marry" the couple that is getting married.
("To get married" does not have this ambiguity.)