The first kind of intrinsic value is contrasted with instrumental value. Instrumental value is the value something has because it's helpful or supportive of something else which has value; think “derivative value.” For example, an important point in how we treat (other) animals is whether there is any reason to consider factors beyond the value of animals to human well-being.
The second kind of intrinsic value is value that is located inside as opposed to outside the thing that is valuable. As Korsgaard put it, “It refers, one might say, to the location or source of the goodness rather than the way we value the thing.”1 This kind of intrinsic value might be, for example, a property of the valuable thing itself which does not depend on anyone in the world valuing it.
So if I claim old trees have intrinsic value, it's not clear whether I'm saying that old trees have non-derivative value or whether I'm saying old trees have value regardless of anyone valuing them. Suppose I personally and directly value old trees. Also suppose that old trees need someone to value them in order to have value. In this situation, old trees have the first kind of intrinsic value but lack the second kind of intrinsic value.
Korsgaard considers the first kind of intrinsic value to be something of a misnomer, since only the second kind of intrinsic value contrasts with extrinsic value. Whether value is derived or not is simply another issue.
1. Korsgaard, C.M. (1983). Two distinctions in goodness. The Philosophical Review. 92(2). [search link]