1. What are the differences? I've no idea what the significance of the source is.
2. The one you linked is hella unreadable. OP's table is, due to the color differences, extremely easy to skim, while the one you linked has only very similar black&white x and checkmark symbols, which require closer inspection to differentiate.
The "main" development site for HTML5 is the WHATWG. That's where all the browser implementors convened when they lost faith in the W3C.
The WHATWG doesn't bother with versions, there will be no HTML6, for example. They just continually update the HTML5 spec. It's a living spec.
The W3C kind of tracks the WHATWG progress and tags certain points with version numbers (that's where the "5.1" comes from).
Although they do some development on their own, and sometimes both sides disagree and the specs diverge. At some point WHATWG removed an element that W3C retained or the other way around.
I have no idea if they still diverge. I just discard the W3C when it comes to HTML5 and follow WHATWG.
Well, practically speaking, I follow what the Mozilla Development Network documents. :-)
I love http://caniuse.com but I wish they had more detail. For instance, on the XHR page, I'd like to know which browsers support addEventHandler syntax and which ones require the use of onreadystatechange.
Note, the reason why there some features in 5.1 that are not in 5.0 is that there are some features not implemented yet, 5.0 only includes implemented features.
The browser-tag relationship often happens to be more nuanced than just “supports” or “not supports”. I'd recommend skimming an MDN article in case of doubt. They also include browser compatibility tables for quick reference and link to W3C and WHATWG specs.
<center>, though, has no semantic implication. <small> can be taken to mean "here be subsidiary information not worthy of large print (or in which we wish to hide critical information we do not with the reader to pay any attention to)". Centred text (or figures) is, and always has been, a stylistic decision, and there are already containers that are semantically meaningful to which that stylistic decision may be applied.
The repurposed definitions of B and I, when everyone remembers them as meaning "bold" and "italic" (and browsers still render them thus), seem really weak to me. SMALL makes sense really only because we have a concept of "small print". I will concede I can't conjure up a similar argument for CENTER, though alongside HEADER (the thing at the top of the page or a section thereof) and FOOTER (the thing at the bottom), it doesn't seem so ridiculous.
And you would mark <i class="foreign" lang="fr">le seule mot juste</i> how? It's not emphasized, introducing a new term, or a citation, but it is traditionally typeset as italic (so simply marking it with a <span> is losing information). Much the same can be said for non-emphasized bold text. <strong> would be wrong. B and I still mean bold and italic respectively, but they are used only to cover the cases not specifically covered by other tags. Markup should be about langue, not parôle.
> it is traditionally typeset as italic (so simply marking it with a <span> is losing information).
"traditionally typeset as" is not information about the content, its information about historical typographical practices.
Ideally, over time, the actual semantics, rather than merely the traditional presentation, of the things where the "B" or "I" tags might be the currently least-bad standard tags would be defined in HTML. Though <span lang="fr"> is already semantically adequate for the specific case you present because the "foreign" is implicit in the span having a different lang attribute than the surrounding content, and the "i" is just an irrelevancy about traditional presentation of foreign-language content.
I can think of an use case for semantic <center> [0]: snippets of text that are somewhat connected to the current text (so they're not an <aside>) but serve a presentational role in the context of the text.
An example:
Now a ghost, Mr. Smith was surprised to see the words on his own gravestone.
HERE LIES
A MAN OF NO VIRTUE
[0]: Now that I'm capable of thinking up obscure cases, I just have to hone my ability to sanctimoniously ignore real needed uses and I'll be on my way to join a standards body.
Agree. And also no valign="middle" in HTML5 <td> elements drives me crazy. I know I'm "supposed" to use CSS, but CSS should be simple. I shouldn't have to fight with silly non-intuitive negative margins and nested div hell just to center something. And then deal with IE's own artistic interpretation of that div hell.