International Border is the line that both countries and the rest of the world have agreed upon.
LoC (Line of Control) is the ceasefire line after the 1948 Indo-Pak war. In the winter of 1947, Pakistan tried to take over Kashmir, forcing the Maharaja of Kashmir signed an accession to India. Pakistan didn't access the accession and fought a war.
Before the Maharaja signed the accession with India, Pakistan's army had already invaded a big chunk of the state. Once the Maharaja signed the deal, Indian army then started fighting, taking back much of the territory. However, before the Indian army could take over all the parts held by the Pakistan army, the Indian leadership agreed to a controversial ceasefire that froze the borders since then.
Plenty of reasons are alleged for the ceasefire - including a brutal winter in the Himalayas, a practical stalemate, inexperienced leadership and the excessive influence of Lord Mountbatten [Britain appointed Viceroy whom India retained even after Independence] who might not have wanted to spoil his legacy with an endless war between the nations he helped create.
Whatever maybe the reason, the fact is that this is the unofficial control line both armies were forced to take. This border is not accepted by either nations as official. India still wants to take back the rest of Kashmir [called Pakistan Occupied Kashmir in India] and Pakistan wants to take back the state of Jammu & Kashmir currently held by India.
In summary, LoC is an unofficial border line that reflect the troop positions of December 1948. Both nations don't want to draw their border with LoC. International Border is an accepted line that both nations use on their maps.
