I read a lot of professional international relations material (but I'm not an expert in any way). IME what may differ the most between 'popular' takes on IR and professional ones is the response to incidents.

Arguably the #1 priority of professional IR is to prevent wars (with occasional exceptions, such as Russia or Hamas recently, but even they want to control when, where, and how). Wars can and do happen whether you want them or not; if you want to prevent them, good will - even on both sides - is not nearly sufficient. You need to understand the mechanisms and operate them effectively. It's not about game theory, but a very human, emotional mechanism:

The fundamental mechanism is politics. The most fundamental theory of warfare, courtesy of Carl von Clausewitz, is that it is "The continuation of political intercourse, with the addition of other means ...", the other means being violence. Warfare is politics, carried out through violence rather than through elections, negotiation, etc.

Another mechanism is the cycle of escalation. You'll see non-experts say, when threatened or attacked, 'we should strike back harder!': It's emotionally satisfying, it feels safer - anger helps people feel safe in danger, and attacking feels powerful; also it sells well politically for those reasons - the politician looks 'tough' and won't be called 'weak'. And here's that fundamental mechanism, politics: Experts know that a common cause of unwanted warefare is the cycle of escalation. Both sides 'strike back harder' - the other side responds just like you do - and the political machine revs higher and hotter, and, well, war is politcs - at a certain point, you can't stop the war. One diplomat I read said, 'the job of diplomacy is to prevent a B-level problem from turning into an A-level problem'.

IR professionals need to find ways to respond - to deter and at the same time for their leaders to succeed in that political machine - without escalating. For example, years ago North Korea did something threatening regarding their nuclear weapons program. I wondered how the US would respond. The US flew a nuclear-capable (but not nuclear armed) bomber from the US, over South Korea, and back to the US. There was no threat to NK from one bomber, but the message was clear - we can reach you from the US (so destroying SK will not protect you), we have vast capabilities you don't and can't stop, we also have nukes, we have a very close relationship with SK, and we are very serious.

Another mechanism that causes warfare is a lack of flexibility, a lack of options. Popular takes on IR love to urge that a 'line in the sand' or 'redline' should be drawn - another tough, angry way to feel powerful and safe. You don't see professionals say it however. For an example of why, remember early in the Syrian civil war when Assad was dropping chemical weapons on their own population. The US publicly announced a 'redline', saying use of chemical weapons would result in (I forget what). Then Assad did it anyway. Now the US was caught - they had backed themselves in to a corner with their redline, taking away their own options. Assad chose their moment to embarass the US, and in the end, the US effectively backed down and lost credibility.

If you have no options, then the other side pulls the strings; they can force you to act when, where, and how they want - and you can assume they will chose the worst possible situation for you. You'll hear professionals say that leaders want options - lots of options. That's why. If you fight or do anything, you want to do at the time, place, and with the means of your own choosing - another phrase you'll hear.

Finally, know that these very sensitive, complex mechanims tend to produce unintended consequences, and there are no take-backs. IR professionals craft responses very carefully and try to anticipate all contingencies, and then hold their breath. If your single bomb accidentally ignites the natural gas distribution network and blows up half the city, nothing will undo that. Even if they don't want to, the enemy will be compelled - by that political mechanism - to respond as if you intentionally burned down the city and killed tens of thousands of civilians, and now you have a possible war and an enemy for generations.

Hope that helps. I wish HN had some professionals in that field to chime in here.