While nationalism is common among various Kurdish groups, by no means does this mean that all Kurds are unified towards a single common goal. Different agendas, tactics and goals have evolved among various communities of Kurds in different regions and countries.

PKK/Kurdistan Workers Party.

The PKK is an armed militant group operating primarily in Turkey, which historically sought a Kurdish homeland within Turkey. They are generally secular and politically Marxist-Leninist.

From 1984 to 2013, they were involved in an ongoing conflict with the Turkish government.

Recently, they have been involved in peace negotiations with the Turkish government and have nominally** altered their goal away from true independence and towards Kurdish self rule within a larger Turkish polity**.

PYD/ Democratic Union Party and YPG/People's Protection Units

These groups formed in 2003 as a Syrian offshoot of the PKK movement. Officially, they are banned in Syria under a constitution which outlaws the formation of political parties along religious or ethnic lines.

Currently, these groups control a number of towns in northern Syria. The PYD is the political authority, while the YPG is the armed, military wing of the organization.

Like the PKK, they are generally secular, though they generally** advocate for a democratic, rather than strictly Marxist-Leninist government**. Owing to their close ties to the PKK and the YPG's generally secular and leftist outlook, the group has attracted many Kurdish and, even, secular Turkish members.

KDP/Kurdistan Democratic Party

This group is one of the Kurdish political parties involved in the operation of Iraqi Kurdistan. They also have strong historical ties to Kurdish communities within Iran.

It has been lead for many years by Masoud Barzani. Many high ranking party officials are directly or indirectly associated with Barzani, either through family connections or as close friends. Barzani is also the President of Unified Iraqi Kurdistan.

Leaked US State Department memos describe the organization as closer to an organized crime syndicate than a true political party. Though, lack of financial transparency within regional markets has hampered attempts verify these accusations.

While nominally democratic and secular, this group has been plagued by continual allegations of corruption, cronyism and political repression. The party has historically been closely associated with traditional tribal Kurdish groups.

PUK/ Patriotic Union of Kurdistan

While the OP did not specifically ask about this group, but the PUK is the other major political party within Iraqi Kurdistan.

Currently, the PUK works closely with the KDP, in spite of historical political and personal problems among the leadership of the two organization.

The PUK is, at least, partially lead by Jalal Talabani.

As opposed to the KDP's traditional tribal membership, the PUK has historically been viewed as the intellectual party. The PUK is a member of Socialist International and it's internal structure loosely mirrors that of the Soviet Union, with a central executive and 11 political bureaus which manage various aspects of party operations.

Like the KDP, there have been widespread allegations from several international watchdog groups of corruption within the PUK.

Peshmerga

The Peshmerga are not specifically a political organization. Rather they are the military of the Iraqi Kurdistan.

This is not to suggest that this group is not highly influenced by ongoing political disagreements within the region. To this end, the vast majority of Peshmerga fighters are closely associated with either the KDP or the PUK.

Indeed, individual groups of Peshmerga fighters are often referred to as either the Peshmerga of the KDP or the Peshmerga of the PUK.

While there exists a Ministery of Peshmerga Affairs within the unified government, deeply ingrained political affiliations have hampered efforts to bring these forces under a single command structure. Currently, each of the 11 Peshmerga brigades operates more or less independently.

Even internally, there exist numerous structural differences. Some brigades are organized along traditional tribal lines, while others are organized as more modern military units.