Seminary refers to an educational program for high school students that provides religious instruction in addition to secular education. Seminary classes are typically taken outside of regular school hours and are taught by lay teachers who are trained and approved by the church.
On the other hand, an institute refers to a college-level program of religious education for young adults and is typically located on or near a college campus. Institute classes provide opportunities for students to study and discuss LDS scripture and doctrine, as well as to participate in social and service activities with other LDS young adults.