A nation is a people with a common history and culture. A state is a territory with a population, borders and a government with the power to exercise its authority within those borders.
Today, most countries are nation-states, combining nations - a people with a common history and culture, and states - having a formal government structure exercising sovereignty within its borders.
But there are also weak states such as Pakistan, which has little power to exercise sovereignty within some of its regions and borders, e.g. Northwest Pakistan. Within Pakistan, some Punjabis, Beluchis and Pushtuns, who are divided by artificial borders originally drawn by the British, claim their own nationhood. Al Qaeda and the Taliban freely cross the border between Pakistan and Afghanistan to work with their fellow Pushtuns. There are also Tajiks and Uzbeks in Afghanistan, with Tajikistan and Uzbekistan right next door.
There are many other mismatches of nations and states.
There are nations without states, such as the Kurds, who are scattered over Iran, Iraq, Syria and Turkey. There are states containing different nations, such as the former Yugoslavia, which later broke up into seven countries. The borders of African states, set by European colonial powers, often have several nations within them. Sudan had an Arab Muslim North and a black Christian and animist South which were in conflict for 30 years at a cost of two million lives. Sudan finally split into two countries, but now the Dinka and Nuer are fighting within South Sudan. Nigeria has 250 ethnic groups and there have been major conflicts among the major Igbo, Yoruba and Hausa tribes. There are unreconciled nations within states, such as the French in Canada, Tibetans in China, and Native Americans and Native Hawaiians in the U.S.