Perisa on the podcast asked what the differences are between logical and metaphysical modality. Jim mentioned he’s becoming somewhat of a modal skeptic (reading Oderberg may do that to you). Leaving modal skepticism to one side, the differences between logical and metaphysical modality are between broadly logical and narrowly logical possibility.
Logical (or broad) modality refers to anything consistent with “the truths of reason,” — which is to say, anything that doesn’t clash with the Principle of Non-Contradiction. Thus, anything that claims to have incompatible sets of boundaries (for example, a square-circle) is broadly logically impossible.
Metaphysical (or narrow) modality (from a Scholastic or Aristotelian perspective, anyway) refers to the natures of things that could not be otherwise without them ceasing to be what they are. For example, to say “water is not H20” is not logically impossible (because it is not contradictory) but it is metaphysically impossible. Water, given its nature, will always be H20. Otherwise it just isn’t water.
There is controversy around these points, of course.