Pains me to say it, but @ProfMattFox made a good point yesterday about the difference between ID methods and non-ID methods. I was thinking about that on my dog walk this morning.
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The distinction seems to be 2-fold. First, a lot of non-ID epidemiology is theory-light. I don't mean that as a criticism. Epidemiologists study the real world and we recognize that it's unfathomably complicated. We won't have an epi version of general relativity.
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In ID, there's a bit more fundamental (germ) theory. For example, for @ProfMattFox to get gonorrhea, he has to ... you get the point. There's a strong (albeit cringy, in this circumstance) theory that allows you to build a model (SIR models and their ilk).
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But there's another distinction between ID and non-ID models that i find interesting. Non-ID models are overwhelmingly statistical models: you collect data, then you fit a model to estimate parameters (simply speaking).
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There's a strand of ID epi that does that too, but the ID models that are getting press right now aren't (generally) statistical. They're based on probability rather than statistics. The model is built by chaining together a slew of conditional probabilities.
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What's the probability you become Infectious in the next time unit given that you're exposed? What's the probability you die in the next time unit given that you're infectious? That's the heart of compartmental models.
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(yes, yes, there are differential equations...but to estimate these you essentially rely on difference equations in one way or another)

total aside/

In this way, the difference between ID epi and non-ID epi methods reminds me of when i taught the phd-level 1st semester stats inference class for epi/env health/health policy students.
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The first 1/3 of class was probability: laws, expectations, distributions. Then we needed to turn the corner to talk about statistics. Turning that corner was always HARD. I remember Andrew Gelman writing that once, so I was glad to have smarter company in feeling that way
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That disconnect is the same as the one between ID epi and non-ID epi. Probability vs Statistics, to put it simply.
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In biostats, there's no fundamental disconnect between probability and statistics. In epi, there is a disconnect between ID and non-ID. I suspect it's because we teach it that way. Non ID methods teachers sidestep ID methods in most courses.
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I have some thoughts for remedying that, but it'll have to wait for another walk.

fin/

oh i'm not totally sure what the appropriate way to add citations is in twitter but my point about non id epi not having strong theories comes, i think, from Sander in this talk:

I'm stopping after this tweet to go hang out with my kids, but i show this video every year in my 3rd semester methods class, @Lester_Domes , and they LOVE it. (or they love me not talking...hard to say)