Most people view Islam, just like any religion, as consisting of a set of thoughts, values and instructions on how best to conduct oneself in accordance to the Will of the Creator; these instructions are what are referred to as the divine rulings or the ahkam shariah - the Shariah for short. The main driving force keeping these thoughts, values and behaviours alive and in circulation is largely inherent, as abiding the Will of the Creator is directly linked in Islam to (a very individual concept of) reward and punishment in the Hereafter. Put simply, if you don't follow the Shariah, you're in trouble. So by and large, Muslims through the centuries have stuck to the Shariah, abiding by its commands, and avoiding its prohibitions. The ruling executive and the jurispudence has in the past generally reflected this by being Shariah-compliant in those matters perceived by the public to be governed by clear Shariah rulings.
But those who also view Islam as a political ideology will see the Shariah differently. Any ideology is seen as comprising a Thought and a Method, with the latter consisting of the manner in which the Shariah rulings are executed, in addition to the manner in which the creed is preserved and the ideology propagated. Such a model necessitates the existence of an executive political entity to carry out and administer the Method, and considers this entity a fundamental part of the Method, and hence of the ideology itself. Consequently, great importance is attached to bringing about this executive authority in a quest to resume the "Islamic way of life" (disrupted by the collapse of the Ottoman Caliphate in the early 20th century).
This is in contrast to the "religious" model above, which considers the political executive entity a natural and inevitable development, as its existence and functioning is itself, like most other matters, governed (to some extent) by the Shariah. While the "ideological" view recognises the fact that any political entity will ultimately reflect the thoughts prevalent in society, they address this by attempting to "politicise" thinking amongst the public so that the establishment of a totally Shariah-compliant state would enjoy broad popular support.
Naturally, the propnents of each view will prioritise their daawah activities according to their outlooks, and their measures of success will reflect this. Despite the differences however, fundamentally, all groups are carrying out what they perceive to be the obligation upon them. Those whose work is focussed on encouraging Muslims to abide by the Shariah, do so out of a belief that this daawah is itself part of the Shariah, and hence worthy of reward. Similarly, those who work to raise awareness of the necessity for an Islamic state only do so out of a sense of Shariah obligation. And those in authority in the Islamic state would rule according to the Shariah, as this would be an obligation upon them, i.e. that would be how they would abide by the Shariah.
But the issue that deserves some more thought here is this: does the obligation upon the ruler to implement the Shariah extend, in his absence, to the Muslim public, making it an obligation upon them to bring such a ruler into existence? By not having the Shariah implemented upon them, are the Muslim masses sinful, even if they abide by the Shariah in other matters?
