Rick,
You may indeed be correct that intentionally designing separate areas with the same ID doesn't actually violate RFC2328, since the document doesn't actually expressly prohibit such designs. On the other hand, it doesn't appear to document intentionally doing so either, even as a "may".
Section 3.7, "Partitions of areas", is worth reading. In summary, it documents what has already be noted in our posts, that partitioned backbone areas are a problem, partitioned non-backone areas should continue to function unless the address range has been split.
As to our assumptions that I consider two areas of the same ID partitioned, where you believe they effectively become two different areas, section 3.7 notes that although two areas of the same ID may effectively still function, they have the "same color". I believe this part of the RFC supports my assumption that two areas of the same ID are indeed a partitioned area and are not the same as two different numbered areas, even if they might function as would two different numbered areas.
Whether intentional design of multiple areas of the same area ID violates the RFC (and I'll again affirm it doesn't appear to) or whether such design violates the "spirit" of the RFC, let's turn to the question of "not best practice".
No one has suggested intentional design of multiple areas of the same area ID is "best practice", but I believe it's "bad practice". "Bad practice" is certainly also "not best practice", but "not best practice" alone, at least to me, means something just suboptimal. "Bad practice", on the other hand, means to me, something to be avoided.
Even "bad practice" doesn't mean never do it, but if you do, you should probably have a very good reason for doing it. For instance, we could have two separate areas of the same ID while we're waiting for some new router or link. I.e. it's only temporary.
Your and Edison's posts certainly address the original question "What is the difference between these two topologies?". But, I think, to the (more important) second original question "Why should I change the Area numbers because the areas 1 are not directly connected.", that just "not best practice", perhaps doesn't sufficiently discourage this practice especially in light of the fact it can be done.
Both you and Edison have the experience to fully understand what's good and bad. I believe, many readers of these posts lack that depth of experience, so you have to be careful when noting "it effectively becomes 2 different areas" might imply to many that you can do something not "described in the book", even if "not best practice". I've seen young engineers looking to do things to demonstrate their abilities will sometimes do things "betcha you didn't know you could do that" without full appreciation of other issues that might be caused later on.
