To the eye of younger folks like me who doesn't know or care exactly why JCT split into two, Series B looks like a specialized journal almost entirely in graph theory while Series A deals with a broader range of combinatorics of mostly non-graph theory kind. There are some overlapping areas such as graph decomposition. But I think they're rare exceptions. The experts in the overlapping areas may have some opinions on this. But as an outsider, I can't see any meaningful difference.
As for your first question, it's not easy to give a good answer everyone can agree for various reasons. One major reason is that it depends on how you define your "tier" and how you evaluate each journal.
For instance, even if you come up with an ideal, objective measure of the quality of a paper, it's still difficult to judge a journal. In some journals, the quality (by your ideal measure) varies greatly from article to article, so if you simply take the average, they might look mediocre even though they publish very good papers as well. Such journals typically publish more papers than picky, selective ones.
Now if you ask me how important a given journal is to my own field, I'd say a very positive thing if it attracts many good papers. But you can also evaluate journals by how difficult it is to "get in." In other words, the term "tier" can be synonymous with "league" as in "She's out of your league" if I'm allowed to employ a potentially inappropriate analogy. In this view, you might say your paper gets rejected because the referees and editor thought they were out of your work's league, and you "scored" a journal when your paper gets accepted by a glamours journal by this kind of standard. I don't think this kind of ranking is well-liked. But it's clearly of use for certain purposes, and this can be what you mean by "top tier journals."
Since you linked to the related MO thread, just look at Anna's and Douglas's answers. Anna ranks Discrete Mathematics among the top journals, and Douglas says,
In my opinion, Discrete Mathematics is only a mediocre journal (I wouldn't consider this top journal). Yes, it contains good papers, but it contains a lot of papers... on average... it's average.
If you read the blog post quid linked to in the comment, it's described as "good solid journal; not of the absolute top rank." I think you can see how people rank journals differently (probably because they have different criteria for a journal to fall in the top tier category). I'd hesitate to call Discrete Mathematics mediocre, but I think Douglas's description is otherwise spot on.
With this caveat in mind, I'll give my personal list of good combinatorial journals. Of ourse, this is going to be inevitably subjective in nature, so read it with a huge grain of salt.
But before that, there are a couple more things you should note. The first thing is that discrete mathematics and combinatorics are a huge branch of mathematics. So, mathematicians from different subfield of DM/Combinatorics may feel different degrees of prestige even if you're talking about the quality of the exact same journal by one specific standard; people can have different opinions about the same subfield. Even if a person is completely objective, the journal's level may be uneven across subfields if the journal's scope is wide. So you should take into account who is expressing their opinion.
The other important thing is that some areas don't follow the typical pure mathematical culture. I'll illustrate this by two journals that would be judged as leading, top tier venues by pretty much everyone in the respective subfields.
Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (Proc. SODA) is on the very top in the ranking you gave the link to. As far as I know (I'm not an expert in this field), the typical topics this publication deals with is considered theoretical computer science by many. In theoretical CS, typically conferences are more prestigious than journals, which is the direct opposite of the pure mathematics culture. This is why a "mere conference proceedings" is ranked among the top journals. And, as far as I know, SODA is a prestigious conference. (If you'er wondering if it's a math journal at all, search for my question on MO about the size of a maximum 3-term progression-free set on MO. You can find a link to an example of very good mathematical papers published in this proceedings. But you're right in that it's a computer science journal/proceedings rather than a mathematics journal. So in the remainder I don't talk about this kind of field where conferences are more highly valued.)
The other example where you should take a different culture into account is IEEE Transactions on Information Theory. It is no doubt the very best journal in coding theory, shannon theory, sequence designs, and whatnot. But it may be unfair to other specialized discrete mathematics journals if you directly compare this journal with them.
This is because, unlike the core part of pure mathematics (whatever that means), the field of electrical/electronic engineering doesn't have "generalist journals" that serve as the prestigious publication venues for every branch. This means that the leading "specialized" journals are the natural choice for highest quality papers that would go to top generalist journals if it were in mathematics.
Coding theory and other branches that IEEE Transactions on Information Theory covers do overlap with EE and CS while it is still a discrete mathematics journal (unless you don't count coding theory and such as discrete mathematics). So, if you look at its impact factor, eigenfactor, and other pseudo-objective measures, IEEE Transactions on Information Theory would look ridiculously good for a "specialized" journal. This is partly because it's actually a specialized journal that often publishes the highest quality papers.
It's true that good math journals also publish some papers that can go to one of those IEEE journals. But I don't think a lot of highest quality papers within the scope of mathematical IEEE/ACM journals are published in the best math journals. Because of its clear leaning toward the kind of mathematics that is typically not the central topics of prestigious math journals, this effect seems much more pronounced than on JCTA and the like that also cover coding theory etc.
Also, the best journals in physics such as Physical Review Letters publish highest quality papers in quantum information theory. IEEE Transactions on Information Theory also covers this field. But it isn't a physics journal per se. If your paper is more about information theory than physics, it wouldn't be strange to publish it in this "specialized" journal if you think your work is of the highest quality. So, this is another reason you can't clearly say it's a specialized journal which is less prestigious than the best generalist journals (although the editors of IEEE Trans. IT expressed concerns about the fact that the journal is losing ground in quantum information). So, you can't really say it's a leading specialized journal in DM/combinatorics although it clearly is in terms of quality, prestige, etc.
So, with this verbose caveat in mind, I think JCTA/JCTB/Combinatorica/IEEE Trans. IT would be on pretty much everyone's top tier journal list. And if one of them doesn't make it, I feel like it's probably because of the person's preference in branches of discrete mathematics.
There are other journals I think can be on someone's top tier list too. Journal of Algebraic Combinatorics and SIAM Journal on Discrete Mathematics come to mind, for example. Also, I wouldn't be surprised if you submit an excellent paper to Electronic Journal of Combinatorics. I'm not an expert, but as an outsider, Random Structures and Algorithms looks pretty good.
I like Discrete Mathematics for the reason I already said, but I know it may not be a top journal depending on exactly what you're asking. Also, journals that cover some niche topics may receive more positive reviews from some (e.g., Journal of Combinatorial Designs and Designs, Codes, and Cryptography), although it can't be "top journals by the vast majority's standards" for obvious reasons.
As I said, combinatorics is wide. So, there are many journals and many subfields I'm not familiar with. So there must be many good journals I failed to mention. And those I mentioned may not be as prestigious to other people. The only way to know the accurate ranking by your standards is to read each journal for yourself.
Oh, I almost forgot. If by EJC you mean European Journal of Combinatorics, then I'd say it's a bit overrated in the ranking you gave. But it's a good, solid journal by any standards in my arrogant opinion, and I wouldn't strongly disagree if others say it's underrated.
Last but not least, take this つ[salt]. You don't believe what a random talking duckling on the internet is babbling about.