Due to 2 likes on me writing a paragraph or two on the History of Kuwait, so here it is:
The town of Kuwait was officially established in 1613 by a bunch of Najdi Bedouins and Arabic traders and merchants due to its importance at the head of the Gulf and its bay. The Al Sabah came to Kuwait not long after a century later along with the Bani Utbah. Sabah bin Jaber, or Sabah I, was chosen to be the representative, or Sheikh, of the old town of Kuwait (Kut or Qurain, as it was called back then). The town was a part of the Khalidi Emirate initially and then fell to the Ottoman forces. Kuwait was established as a "Kaymakam" in within the Ottoman Vilayet of Basra (Which is where the Baathists are supporting their claim in Kuwait). However Kuwait was forced into the Vilayet due to organisational and logical reasons, however the Sultans in Constantinople gave Kuwait Kaymakam status to give them considerable authority due to them being quite different, from the rest of the Basra Vilayet. Also note that Kaymakam is considered as a "second-level" province within the Ottoman organisational structure. The Al Sabah continued to rule Kuwait as they saw fit without any intrusion by the Vilayet of Basra. This harmony was cut short however when around the late 1800s Basra, and some Ottoman elites, wants to fully integrate Kuwait into the Vilayet, this caused many in Kuwait, including Sheikh Mubarak the Great, fear that their autonomy would be stripped away from them. This changed however when Sheikh Mubarak successfully got the British to stop such a thing to happen after Sheikh Mubarak signed a treaty with the British in 1899 that effectively severed Kuwait from the rest of the Ottoman Empire.
Also note that Kuwait was, and still is, a very diverse place where trading from Kuwait to all the way to Southeast Asia brought with them new people and cultures that would eventually mould Kuwait into a radically different culture in terms of Language, Culture and Politics. So much so we are considered even a bit different from our GCC brothers.
The fact Saddam, and many before him actually, tried to claim Kuwait and Kuwaitis to be Iraqis is complete act of Hubris by Saddam and his elite. You can see a great deal of difference when you cross the border and go to Basra. Kuwaitis do not consider themselves to be Iraqi, not in 1610, 1899, 1961 nor 1990.
Also consider the Iraqis' lack of knowledge of Diwaniyas and Gengeveh prior to the 1990 occupation as further proof of significant cultural difference between us.