a. Kim has courage.
b. Kim has a car.
My question: Is there a known linguistic concept that captures the difference (that I seem to be detecting, as explained below) in the usage of the verb has in these two sentences?
What CGEL says
According to CGEL (p. 111), the verb has in [1a] and [1b] appears in the same function, which they call 'stative' (the actual example CGEL gives is She has many virtues/two sons). But it seems to me that there is something quite a bit different in the way has functions in these two sentences---maybe not syntactically different, but certainly semantically. I'll try to explain what I mean in two different ways.
Explanation of what I mean in terms of 'linking verbs'
I understand that linguistics does not find the category of 'linking verbs' a useful one (or even a well-defined one), as has been discussed e.g. here. But if we suspend our disbelief (if any) in linking verbs for a second, we might want to say that in [1a] has acts as a linking verb, whereas in [1b] it does not.
It is true that 'linking' to lone adjectives (as in A rose is red) is a hallmark of linking verbs (as traditionally defined), and yet has can never 'link' to (or be followed by) a lone adjective---at least as far as I know. But it is also possible to 'link' to noun phrases. So, for example, in
 a. Kim is a zombie
b. Kim has a zombie,
[2a] is predicating of Kim that it has a certain property, namely, that she is a zombie. If you ask the question, "How many 'entities' are implied to exist by this sentence?", the answer is one, namely Kim. The zombie is not a separate entity; the zombie is Kim. All of this is very consistent, I think, with what friends of the concept of linking verbs would say is characteristic of that category. Also, the verb is in [2a] can be replaced by another linking verb (some that would work include remains, seems, becomes, turns, ...), and the resulting sentence not only makes sense, but its meaning is, in some sense, related to the meaning of the original sentence with is.
In contrast, the sentence [2b] implies the existence of two entities: Kim and the zombie. It further says that a certain relation exists between, namely that of 'having', or of 'ownership', or of 'possession'.
Explanation of what I mean in terms of properties vs two-term relations
An alternative explanation is to say that in [2a], has expresses a property (or a one-term relation) of Kim's, whereas in [2b], it expresses a two-term relation between Kim and the car. Properties and relations belong to analytic philosophy (for relations, see the section relations). They are (therefore) accompanied by one or another degree of controversy, so they are not the firmest foundation on which to build an analysis (which should be, well, scientific, or so one would hope...). But I haven't yet figured out a better way to explain why I think [1a] and [1b] use has in rather different ways.
Now what about ?
The sentence [1b] clearly implies the existence of two 'entities', Kim and the car, and asserts that the relation of possession exists between them. Things aren't as clear in [1a]. You could, I suppose, say that courage is also an entity, and that has again expresses a two-term relation. But that is not at all my 'mental picture' of [1a]. When I say that Kim has courage, I mean that Kim is courageous, no more and no less. To my mind, there is no action of possessing here that is in any way comparable to the clear case of possession in [1b].
Further evidence that [1a] is different: if has is replaced by at least some of the verbs that are traditionally thought of as linking verbs, the sentence that results is at least marginally sensical, and moreover its meaning (such as it is) is related to the meaning of the original sentence. Consider e.g. replacing has by is: Kim is courage. I agree that it is somewhat dubious whether this makes sense. But it can be fixed by expanding it to Kim is the very definition of courage, which definitely does make sense. And this expanded version would also work with is replaced by seems, becomes, remains, and many other traditional linking verbs. Substituting has back produces Kim has the very definition of courage, which is again a bit dubious, but becomes less dubious if replaced by Kim has what is the very definition of courage.
This process does, in fact seem to reach a fixed point. Both of the following seems grammatical, sensical, and in fact mean the same thing:
 a. Kim is what seems to be the very definition of courage.
b. Kim has what seems to be the very definition of courage.
I take this to be evidence that at least in , has is as much a 'linking verb' as is is.
So while the replacement of has by other linking verbs and vice versa (in sentences like [1a]) certainly does not go through completely smoothly, nevertheless there does seem to be some sort of pattern there. It is just a bit trickier a pattern than what we are used to with traditional linking verbs.
The verb has seems to serve two rather different functions in [1a] and in [1b]. Those who like linking verbs might say that has is a linking verb in [1a] but not in [1b]; those who like the philosophical concepts of properties and relations might say that in [1a] has expresses a property of Kim's (that she is courageous), while in [1b] it expresses a two-term relation (one of possession of a car by Kim). Either way, something seems to be relevantly different about has in [1a] vs in [1b]. My question is: is there a known linguistic concept that captures this difference?
A bonus question for those who like the concept of linking verbs: do you agree that has in [1a] is a linking verb?