Logical Versus Metaphysical Modality

A short answer first.  Yes, there are these distinctions.  They amount to a distinction between logical modality and metaphysical modality.  The first is also  called called narrowly logical modality while the second is also called broadly logical modality.   Both contrast with nomological modality. 

Now a long answer.  The following nine paragraphs unpack the notion of broadly logical or metaphysical modality and contrast it with narrowly logical modality.

1. There are objects and states of affairs and propositions that can be known a priori to be impossible because they violate the Law of Non-Contradiction (LNC). Thus a plane figure that is both round and not round at the same time, in the same respect, and in the same sense of 'round,' is impossible, absolutely impossible, simply in virtue of its violation of LNC. I will say that such an object is narrowly logically (NL) impossible. Hereafter, to save keystrokes, I will not mention the 'same time, same respect, same sense' qualification which will be understood to be in force.

2. But what about a plane figure that is both round and square? Is it NL-impossible? No. For by logic alone one cannot know it to be impossible. One needs a supplementary premise, the necessary truth grounded in the meanings of 'round' and 'square' that nothing that is round is square. We say, therefore, that the round square is broadly logically (BL) impossible. It is not excluded from the realm of the possible by logic alone, which is purely formal, but by logic plus a 'material' truth, namely the necessary truth just mentioned.

3. If there are BL-impossible states of affairs such as There being a round square, then there are BL-necessary states of affairs such as There being no round square. Impossibility and necessity are interdefinable: a state of affairs is necessary iff  its negation is impossible. It doesn't matter whether the modality is NL, BL, or nomological (physical). It is clear, then, that there are BL-impossible and BL-necessary states of affairs.

4. We can now introduce the term 'BL-noncontingent' to cover the BL-impossible and the BL-necessary.

5. What is not noncontingent is contingent. (Surprise!) The contingent is that which is possible but not necessary. Thus a contingent proposition is one that is possibly true but not necessarily true, and a contingent state of affairs is one that possibly obtains but does not necessarily obtain. We can also say that a contingent proposition is one that is possibly true and such that its negation is possibly true. The BL-contingent is therefore that which is BL-possible and such that its negation is BL-possible.

6. Whatever is NL or BL or nomologically impossible, is impossible period. If an object, state of affairs, or proposition is excluded from the realm of possible being, possible obtaining, or possible truth by logic alone, logic plus necessary semantic truths, or the (BL-contingent) laws of nature, then that object, state of affairs or proposition is impossible, period, or impossible simpliciter.

7. Now comes something interesting and important. The NL or BL or nomologically possible may or may not be possible, period. For example, it is NL-possible that there be a round square, but not possible, period. It is BL-possible that some man run a 2-minute mile but not possible, period. And it is nomologically possible that I run a 4-minute mile, but not possible period. (I.e., the (BL-contingent) laws of anatomy and physiology do not bar me from running a 4-minute mile; it is peculiarities not referred to by these laws that bar me. Alas, alack, there is no law of nature that names BV.)

8. What #7 implies is that NL, BL, and nomological possibility are not species or kinds of possibility. If they were kinds of possibility then every item that came under one of these heads would be possible simpliciter, which we have just seen is not the case. A linguistic way of putting the point is by saying that 'NL,' 'BL,' and 'nomological' are alienans as opposed to specifying adjectives: they shift or 'alienate' ('other') the sense of the noun they modify. From the fact that x is NL or BL or nomologically possible, it does not follow that x is possible. This contrasts with impossibility. From the fact that x is NL or BL or nomologically impossible, it does follow that x is impossible. Accordingly, 'NL,' 'BL,' and 'nomological' do not shift or alienate the sense of 'impossible.'

9. To appreciate the foregoing, you must not confuse senses and kinds. 'Sense' is a semantic term; 'kind' is ontological. From the fact that 'possible' has several senses, it does not follow that there are several species or kinds of possibility. For x to be possible it must satisfy NL, BL, and nomological constraints; but this is not to say that these terms refer to species or kinds of possibility.