theory

Nice. So use-value relates to use, and exchange-value relates to exchange. That's a good starting point, but still seems a bit murky ... both definitions refer to "value" but in seemingly different meaning... can you explain that difference in meaning?

I think these two paragraphs give an initial description of the two, although Marx indicates it is incomplete:

Two things that jump out at me:

1. Marx oscillates between use-value being something commodities are and something commodities have as a property (being versus having). So depending on context, a commodity is a use-value, or it has use-value.
2. Exchange-value is a relation between commodities, so unlike use-value, we are no longer talking about a single commodity in isolation.

This is really good.

In defining exchange value, you point to the way that commodities gain value but I think it could be a little more exact. Apologies in advance for emoji use but I find it easier to follow visually.

Exchange-value is a relation between two commodities, e.g. “2 🍎 = 1 🍌”. That entire equation is an exchange value. This equation implies two things:

1. Quantitative equivalence. There is a thing or “substance” that is common to both 🍎 and 🍌, and the amount of this substance in 1 🍌 is equal to the amount of the substance in 2 🍎
2. Qualitative equivalence. That substance is qualitatively identical in both 🍎 and 🍌. This is required so that the quantity can be compared, like converting lengths to be in centimeters before they can be summed up.

That third thing, the common substance is value. Value is the thing being expressed in an exchange value.

As an analogy, instead of exchange value and value, think about weight and mass. Mass is the substance of an object which is expressed through its weight. When you put two objects on a scale, you abstract from the qualitative difference of the things and consider them only as masses.