I am not an expert on Shia faith so I'm sorry but Id rather not address that first bit. The best I can say is that they developed over time for various reasons, both proactive and reactionary to historical events. For example, the observation of Ashura by Shias is directly linked to the massacre at Karbala.

The second part I can answer however. Historically, Shia have existed in pockets throughout the Muslim world. Certain Shia orders however have however taken over and ruled states such as with the Fatimids outta Egypt. This is what happened with Iran. Historically, Iran was Sunni. In fact, it was a major Sunni power base for a very long time. That all changed with one movement, a militant-religious order known as the Safviyya. They were Sufis (mystics) of mixed origins who went on to establish the Saffavid Empire in Iran under Shah Ismail. This state went on to actively convert all of Iran to shi'ism and that has stuck to this day. Pakistan as per your example never had any such revolutionary movement.

What actually separates these countries? Well, heres the thing. While Sunni and Shia differ on some points, over all in the broadest terms they are not that different. The pray to the same God, and live by the same holy book. But over time, for various historical reasons as I've mentioned, they (the shia) have gone on to develop a differing self identity and nuanced practices. Again, in both proactive and reactionary terms. The current conflict is not over who should've succeeded Muhammad. The current conflict is over self-inflicted divisions and quarrels between the two peoples that have developed over a very, very long time.

In other words, you are absolutely right. The distinction in so far as conflict and enmity goes is rooted in politics between people with herd like mentalities, not theology or faith or who should've ruled a a long gone empire.