Are all movements of political Islam identical?

Definition of Islamism
It is important to note first that Islam is a religion, but Islamism (often called Political Islam) is something else. It is a political ideology whose goal is to bring the religious tenets of Islam into the daily functioning of a government and its laws. Islamism is a modern movement whose roots began contemporaneously with the rise of Salafism in the late 1800s and early 1900s in Egypt. Islamism is not by nature violent or expansive. Many Islamist movements have concrete nationalistic goals such as the Islamists in power in Turkey.

Meat of the Question
No. They are not all identical. As a result of the doctrinal disputes among Islamists, they divide along two main lines, whether their ambitions are national/international and whether their method of political ascendance is democratic/militaristic. They also vary along a spectrum of how stringently they wish to implement Islamic Law.

National / International Divide
This is a rather simple divide to explain. There are a number of Islamist groups and organizations that specifically target the government of one country and there are a number of other Islamist groups and organizations that target numerous different governments with a singular aim. The former are usually political parties or Islamist groups that have held power at a point of time in the country's history. The latter category are often seeking some kind of Islamic Caliphate, either that controls a significant percentage or all of the Islamic World or the entire planet.

Democratic / Militaristic Divide
A "Democratic" group believes in using any means to advocate for Islamism without resorting to violence. The most obvious way to do this is by fielding political parties with Islamist candidates. However, in addition to elections there are numerous other ways to influence society to embrace Islamism or aspects of it such as: lobbying, peaceful protests, information outreach to other communities, welfare projects, societal organizations, television/radio/internet programming, using social media, and live debates. The "Militaristic" group is commonly defined by an ideology called Jihadism since these groups believe that only through a Lesser Jihad (Islamic Holy War) can an Islamist State be brought into existence. Whether or not the violence perpetrated by these groups conforms to Lesser Jihad as determined by Islamic Jurisprudence is hotly debated by both Muslims and Non-Muslims, but the "Militaristic" groups support the view that these wars are a form a Lesser Jihad across the board.

Some Examples

National Democratic: There are a number of localized political parties that have national Islamist agendas and who exclusively use elections and other non-violent means to attain power. Among these are the AKP in Turkey, the an-Nahda Party in Tunisia, and the an-Nur Party in Egypt. Some of these parties, like AKP and an-Nahda have a moderate view of the Shari'a (Islamic Law) and therefore are less stringent in what they would like to see implemented from the Shari'a. Others like the an-Nur Party are very stringent.

International Democratic: There are several international organizations with the goal of Islamism that export it without necessarily involving violence. Probably the most prominent of these is the Muslim Brotherhood. While the Brotherhood has embraced violence in certain places, most notably in Palestine where the local Brotherhood chapter is the Hamas Paramilitary/Terrorist group, it is generally committed to peaceful protests in numerous countries where it is active. Another such group is Hizb at-Tahrir. Both parties have the goal to implement Islamism worldwide.

National Miitaristic: There are quite a number of Jihadist groups with particular local goals. The Taliban in Afghanistan wish to rule exclusively over Afghanistan and Pashtun-majority parts of Pakistan. They have no ambition to conquer any neighboring territory or export their ideals outside of this region. Another similar group was the Azawadi Jihadists (especially Ansar ad-Din) which have a goal of conquering only the majority Touareg areas in Mali.

International Militatistic: These are the most infamous Islamist groups and Jihadist organizations. They all have a dream of a worldwide Islamic Caliphate and include such members as al-Qaeda, ISIL (Islamic State of Iraq and the Levant), al-Shabaab in Somalia, and Hezbollah (in certain aspects). Because their ideology has such providential significance to them, every International Militaristic group has a very stringent view of Islamic Law that they wish to implement.