I like to think in terms of two SOF "trinities" (and in particular for the SF, CA, and PSYOP elements of SOF).
(Note: All great concepts come in threes: Fear, honor, and interest; passion, reason, and chance, (or people, government, and the military); life, liberty, and the pursuit of happiness; federal democratic republic; the legislative, executive, and judicial; federal, state, and local; presence, patience, persistence; political defiance, political resistance, and political violence; ends, ways, and means; strategic, operational and tactical, and many more.)
The first: Irregular Warfare, Unconventional Warfare, and Support to Political Warfare.
The second is the comparative advantage of SOF (and in particular, SF, CA, and PYSOP): governance, influence, and support to indigenous forces and populations.
I prefer the 2018 NDAA definition over the DODI 3000.7 definition of Irregular Warfare:
Congress (2018 NDAA): US military forces and the interagency conduct operations "in support of predetermined United States policy and military objectives conducted by, with, and through regular forces, irregular forces, groups, and individuals participating in competition between state and non-state actors short of traditional armed conflict."
DODI 3000.7 definition: "violent struggle among state and non-state actors for legitimacy and influence over the relevant populations."
I think we all know the UW definition (in JSC Pub 1-02/3-05) that was re-written in 2009. "activities conducted to enable a resistance movement or insurgency to coerce, disrupt or overthrow a government or occupying power by operating through or with an underground, auxiliary or guerrilla force in a denied area." Note that I use the revised definition that was in the 2016 NDAA, Section 1097 that said "OR guerrilla force" versus "AND guerrilla force". We wanted "or" in the definition because in modern UW there may or may not be a guerrilla force -there may only be an underground and auxiliary. But the traditionalists demanded "and" because they said the essence of UW is guerrilla warfare and without a guerrilla force you cannot conduct UW. Note the Joint Staff and DOD will not change the definition to match what Congress wrote.
Lastly is support to political warfare.
I think George Kennan and Paul Smith have described Political Warfare very well and I think the USASOC White Paper describes SOF support to political warfare:
George F. Kennan defined political warfare as "the logical application of Clausewitz's doctrine in time of peace." While stopping short of the direct kinetic confrontation between two countries' armed forces, "political warfare is the employment of all the means at a nation's command... to achieve its national objectives." A country embracing Political Warfare conducts "both overt and covert" operations in the absence of declared war or overt force-on-force hostilities. Efforts "range from such overt actions as political alliances, economic measures..., and 'white' propaganda to such covert operations as clandestine support of 'friendly' foreign elements, 'black' psychological warfare and even encouragement of underground resistance in hostile states." See George Kennan, "Policy Planning Memorandum." May 4, 1948.
http://academic.brooklyn.cuny.edu/history/johnson/65ciafounding3.htm
Political warfare is the use of political means to compel an opponent to do one's will, based on hostile intent. The term political describes the calculated interaction between a government and a target audience to include another state's government, military, and/or general population. Governments use a variety of techniques to coerce certain actions, thereby gaining relative advantage over an opponent. The techniques include propaganda and psychological operations (PSYOP), which service national and military objectives respectively. Propaganda has many aspects and a hostile and coercive political purpose. Psychological operations are for strategic and tactical military objectives and may be intended for hostile military and civilian populations. Smith, Paul A., On Political War (Washington: National Defense University Press, 1989)
https://apps.dtic.mil/dtic/tr/fulltext/u2/a233501.pdf
USASOC White Paper: SOF Support to Political Warfare:
A whole-of-government endeavor, Political Warfare is best led by agencies beyond DoD and can only succeed if it is conducted in a way to "elevate civilian power alongside military power as equal pillars of U.S. foreign policy."
SOF is well suited to lead DOD's contribution to Political Warfare's activities, because they are relatively knowledgeable experts in this form of warfare
The overall Political Warfare effort relies on persuasive and coercive diplomacy, economic coercion and engagement, Security Sector Assistance (SSA), Unconventional Warfare (UW), and Information and Influence Activities (IIA).
Tier 1 and Tier 2 forces and the CT/DA missions are critical to our national security and they are essential elements of SOF but what I outlined above is really the heart and soul of SOF (and in particular SF, CA, and PSYOP forces which make up the bulk of SOF).