What is the difference between Presbyterian and Free Presbyterian?

Answer 1

The Free Presbyterian Church is an offshoot church of the Presbyterian Church of Ireland.
The FPC separated from the Presbyterians due to a theological dispute; and personal and ethical conflicts between church elders.

Answer 2

There are actually many Presbyterian denominations. The Presbyterian Church (USA) tends to take bold positions in areas of social justice, including issues of human rights and stewardship of the earth. Equality among individuals is emphasized without restricting election for ordination to any offices of the church, including both teaching and ruling elder, by gender, age or ethnicity. The PC(USA) holds the Hebrew and Christian Scriptures to be unique, authoritative and inspired, while maintaining a tension in the church between those who believe that The Bible is inerrant and those who do not believe in inerrancy; both views are welcome. Other Presbyterian denominations vary on their view of the role of women in the church. The Evangelical Presbyterian Church leaves the decision of ordination of women as teaching elders to the individual presbyteries, and the ordination of women ruling elders to individual congregations. Woman are accepted as deacons. The Associate Reformed Presbyterians will ordain women deacons, but not as ruling or teaching elders. The Presbyterian Church in America and the Orthodox Presbyterian Church will not ordain women to any church office.