I know you are asking for a semantic answer but I will instead adopt a syntactic approach.
Why ? Because as an answer to your question, I would tend to say :
no, because they are both semantically empty.
I will support my claim using a major DM-style assumption, namely that there is no essential difference between inflection and derivation.
The difference between the genitive and relational adjectives pertains to functional (as opposed to semantic) content.
Relational APs are, by definition, never predicative (cf. 1), which may be predicted by assuming them to lack the semantic PredP layer and only retain the functional aP layer.
(1) # Hic pes est equinus. 'This foot is equine.'
The genitive, in turn, may be regarded as semantically similar to English of and was later replaced by Vulg. Latin de : it expresses the vaguest relation possible, and may be interpreted in various ways according to the context -- quite similarly to what accusative case does with the Verb, since the object of a Verb may denote whatever thematic role is needed ; the genitive is, somehow, the direct case of the Noun -- hence the idea that such projections are purely functional.
Strikingly, the only way (1) may be interpreted is by relating it to (2).
(2) Hic pes est equi. 'This foot is that of a horse.'
That is, in both cases the predicative use coerces the structure into receiving a non-vague interpretation, and it seems to be encoded at least in the adjective as a structural variation since it is reflected in the grammar, e.g. by the fact that relational adjectives are usually found after the N :
- a. pes equinus / ? equinus pes
- b. furnus aeneus / ? aeneus furnus
Such analogy, it seems to me, supports a hypothesis of GenP and aP as semantically null, purely functional projections, the only difference being that the complement of Gen is always a NP/DP, while aPs need not embed a nP unless they are relational (= little a may attach to a bare Root), cf. (4) .
- a. # Hic pes est equinus.
- b. Hic pes est magnus.
In (4a), A is relational, and as such, necessarily denominal. We have a [aP [nP √]]-style structure. This correlation is similar to what we find with the genitive.
In (4b), A is predicative and as such, not necessarily denominal : here we likely have a structure more like [PredP [aP √]].