"specifically targeted" and "targeted specifically" mean the same thing.

In both expressions, "specifically" modifies the verb - targeted.

We can see some other OG questions as well in which adverb is placed before or after the verb:

1: Unlike the honeybee, the yellow jacket can sting repeatedly without dying and carries a potent venom that can cause intense pain. (OG12 Q#20)

2: Eating saltwater fish may significantly reduce the risk of heart attacks and aid sufferers of rheumatoid arthritis and asthma, according to three research studies published in the New England Journal of Medicine.(OG Verbal Edition 2 - Q#28)

The two instances that you are comparing are not exactly comparable. In the previous post, we were talking about the following:verb adverb vs adverb verb

When it comes to this kind of placement, both typically imply the same meaning as long as there is no ambiguity in meaning. The ambiguity may happen if there is some other verb in the sentence and the placement of adverb is such that its no longer clear what the modifier modifies.

In OG#70, the issue is exactly that. Lets review the incorrect choice structure:

Clause A: ..when great ice sheets existed in areas now
Clause B: that are temperate.

The placement of "now" in Clause A is such that "now" describes the verb - existed. This is non-sensical. The verb "existed" describes an event that took place way back in the history. Using "now" with this verb is incorrect and illogical.

Lets consider a similar sentence: In the example below, both sentences are logical but they imply different meanings.

The mouse ran swiftly away from the cat that ran after it.
The mouse ran away from the cat that swiftly ran after it.

Thus, the key thing to remember with adverbs is that they are pretty flexible in terms of their placement, with the only caveat that there should not be any confusion about which verb this adverb refers to.