is an interaction enough to collapse a wave function, or must one make a measurement and, if so, what is the crucial difference?
A measurement is a special kind of interaction. And not all interactions are special enough to call them measurements.
An interaction is basically anything that involves waiting. But if that's too general and you want to say it is waiting, where things change. Then unfortunately a measurement might not be an interaction becasue they don't always change something. For instance if you repeat the same measurement twice depending on how you do it, you might not change it the second time. For instance if you get to measure something in a lower versus a higher state by trying to get it to absorb a photon and transition to a higher energy state and its already in the higher energy state, then the measurement might not change anything.
So interactions are quite general, and almost anything is an interaction. A measurement is an interaction. And measurements definitely have the potential to change things so they aren't a passive reveal of preexisting information. But you are asking what makes something a measurement.
And that lack of change upon repeat that is actually a key to being a measurement. A lack of reversibility is another key. Let's talk about both.
First, the repetition. This isn't about repeating the entire experiment again (don't redo the sample preparation and the interaction) just take the actual thing that you measured and measure it again. And measuring the second time doesn't change it.
So you need to have a measurer and a measuree and if you make them interact twice in a row then the second interaction needs to not change the measuree. And also you need to be able to classify every possible thing as a measurer of some type (or not a measurer of any type) and if you take the measuree and take two measurers of the same type and have the measuree interact with one measurer and then interact with the second measurer of the same type then the measuree needs to not change the second time.
So that's a key, and not all interactions do that, and not everything can be a measurer but if you take every measurer (every thing that when it interacts twice with something, doesn't change it the second time) then you can classify them into types based on the equivalence class of not changing something the second time when using first one then the other in either order on any object.
So we can partition the world into measurers that doing them twice doesn't do anything the second time and group them based on being interchangeable for the interaction in this respect. And now measurement is almost just this kind of interaction.
But we also need a kind of irreversibility. When you use a measurer the first time it does have the ability to change the object being measured (it can change the measuree). But to be a true measurement the interaction needs to change something else too.
It's like when you observe something. You have to be open changing yourself to truly observe. If something passed through you and you were the same regardless of what it was, then you didn't really observe it.
So with a measurement you also have to observe which means the different post-interaction results have to each be connected to different post-interaction states of something else.
And the final key is this combination of something being x and something else observing it being x needs to be really distinct in an irreversible way from the measuree being y and something else seeing it being y.
And technically Quabtum Mechanics and its interactions are reversible, so the irreversibility is really about it being impractical to effect the different outcomes (being x and seen to be x versus being y and something seeing it be y) to notice each other. They each have to act as if they each were the only outcome.
So you have the repeatability and the effective irreversability. And having both is what we assume is happening in an interaction when we call it a measurement.