Here are some definitions:
Post (5) preposition
Subsequent to; after: American poetry post the 1950s hasn’t had the same impact
Before (1) preposition
During the period of time preceding (a particular event or time): *she had to rest before dinner the day before yesterday
Before (2) preposition
In front of: Matilda stood before her, panting
Consider the concept before.
Imagine travelling along Pall Mall, passing Suffolk St first, then Whitcomb St. If you were to pause between the two streets, which street is before you? You might say that Suffolk St came before, or that Whitcomb St lies before you.
Came before references history in this context, so we use before (1) to say that Suffolk St is before you. Note that the same words "came before" can also be used to reference position, leading to a similar example to that in the definition of before (2).
Lies before references position, so before (2) applies. In this context, Whitcomb St is before you.
Post also has seemingly contrasting senses, but the apparent conflict can be resolved more cleanly.
Imagine making a (sequential) list of whatever you encounter. Then items later in the list are said to be post the ones earlier in the list.
Consider your first example. Suppose you got a dolphin to swim past an inspection point, noting the fins encountered at the inspection point. The antero-dorsal appears before the postero-dorsal, so they are written in that order on the list. In this sense, the postero-dorsal is justifiably post.
Consider your second example. Now you're walking through history, encountering the modern era before the postmodern. Hence postmodern is written later in your list, justifying the label post.
These seemingly contradictory uses of post stem from the intrinsically opposite order you get, depending on what is considered to be moving: the viewer or the viewed. This also explains your delightful comment that "before ... and after would convey about the same meaning", when we would normally think of them as conveying opposite meanings.