If the people doing the "arranging" in the marriage aren't the parents, that's a Bureaucratically Arranged Marriage.
Often involves Prince Charmless and Rebellious Princess.
Additionally, the "Marriage Before Romance" trope often went hand-in-hand with arranged marriages.
While the priority is, again, the union of two families, that union is dependent on the stability and comfort of the two people getting married, so the two families would try their best to come up with a Perfectly Arranged Marriage.
(Of course, being Big Damn Heroes, they'll have to do so in the most overblown and dramatic way possible.) Sometimes, the person in the arranged marriage takes matters into their own hands and becomes a Runaway Fianc.
For most of human history, arranged marriages were the norm because "marriage" was less about the union of two souls and more about the union of two .
The rise of the "Marry for Love" ideal didn't really start in Western culture until the 16th century, and there are places on Earth where it still hasn't.
A Shotgun Wedding is a short-notice forced marriage.
If someone agrees to an Arranged Marriage but loves someone else, Courtly Love may be involved.