After the First Kashmir War, a series of skirmishes and border disputes followed, culminating in the Second Kashmir War in 1965. Both India and Pakistan point the finger at each other for the blame for eliciting the war. Although the war was elicited indeed by India who attempted to reclaim the part of Kashmir that Pakistan had occupied since the last war, India claimed that Operation Gibraltar, a covert infiltration by Pakistan in Kashmir that was aimed at creating a revolution, had led to India retaliating by invading Pakistan.
The war lasted only 5 weeks, but losses on both sides were heavy, and eventually the United Nations stepped in to call for an unconditional ceasefire from both nations. The aftermath of the war created resentment within Pakistan, specifically East Pakistan (present day Bangladesh) as they accused the Pakistani government of not providing adequate forces to them even though a lot of funds were taken from East Pakistan to finance the war.
Again, the only "global impact" was the UN's intervention to call for a cessation to the war. It was yet another local war, caused by another Kashmir squabble. However, the war had a profound impact on Pakistan as East Pakistan was increasingly resentful towards the Pakistani government's reluctance to help them during the war. It would be the source of tensions within Pakistan that would eventually segregate it from within. Nonetheless, Indo-Pakistani relations continued to deteriorate with the stalemate keeping both countries at bay.
The Second Kashmir War was more of a repetition than the first one, with the same reasons, the same conclusion - an unresolved stalemate. Prior to the birth of India and Pakistan, the two countries were under the single colonial rule of Britain. The separation that came about as Britain left was also religious in nature as Pakistan was principally a Muslim country while India was a Hindu one. The syncrestic nature of both Hinduism and Islam is speculated to be the reason for the incompatibility of the two nations. While India claims to be a secular state, Pakistan is a highly religious one, prompting the two countries to have diverse beliefs and governments. From this dichotomy eventually arose conflict which had escalated into war after a territorial dispute over Kashmir that was notably caused by religious factors.