Nope,
definitely not one Markdown. Reddit uses three different engines with major mutual incompatibilities and mostly forbids all HTML (which frankly I deem enough to call it not real Markdown); Stack Overflow uses two with what used to be critical deficiencies and incompatibilities in the one used for comments, but I think they’re now mostly minor only; some things still use Markdown.pl which does many bizarre things; some, other weird engines with idiosyncrasies of their own; most more recent Markdown engines are only
mostly CommonMark-compatible, regularly deviating in important places, and
very often adding incompatible extensions. It’s a
disaster at present, and I don’t expect it to get much better for at least a decade, if ever. (HTML got better with HTML5, but I don’t think Markdown is likely to unite so firmly, because people want more than non-HTML Markdown offers, and so will continue to extend it.)
HTML, though? Since the HTML5 spec about a decade ago, there has only been one HTML, with all browsers parsing and handling documents identically. CSS is similarly parsed and interpreted according to well-defined algorithms now. There are some visual rendering differences between browsers in how CSS is handled, but it is exceedingly rare for them to affect the content.
And for your complaints about CSS, it’s not intended as a single thing to implement in one piece—it’s deliberately designed as something that is extended over time. But if you write CSS that works in browsers now, then presuming you haven’t used vendor-prefixed stuff, it’s reasonable to expect it to work the same way indefinitely.