Slack has nothing to do with Markdown. The plain text that its text box turns into formatting bears no resemblance whatsoever, and I don’t believe you can interact with it as lightweight markup anyway.

The page you linked says "This formatting is similar to Markdown markup" so it has something to do with it. Given paragraphs, quotes, lists, and code are interchangeable it is certainly regrettably that links, bold, and italic are different but *bold* vs **bold** is still a meaningful resemblance in my book.

Similarities: _…_ for italics, `…` for code, ```…``` for multiline code (… though this is an unofficial syntax not part of Markdown, though it’s very close to ubiquitous), <…> for delimiting URLs, a > prefix for quotes (which is the most common syntax by far, since it was established decades earlier in email), and entity-encoding of &, < and > for some reason (which, given that they don’t support any other entity-encoding, and don’t use the ampersand, and don’t support escaping any of the rest of the syntax, is all-round weird, like although they weren’t actually following Markdown anywhere else they decided to in this one place for some reason and made a total hash of it).

The only similarities that are not extremely common conventions independent of any specific lightweight markup language are triple-backtick code fences, and entity-encoding.

Differences: no paragraphs, line breaks are hard rather than soft breaks, *…* for bold (in Markdown that’s italics, and **…** or __…__ is bold), lists (apparently this syntax doesn’t actually support lists, driving home how this isn’t even Slack’s “normal” format—I’m not sure how lists are actually implemented, given that you can produce them in the web UI), links, strikethrough, emojification, and all the other stuff from Markdown that’s missing (including any other form of escaping or entity-encoding).

Seriously, the resemblance is very superficial. The name is the part that’s closest, by a considerable margin; not the actual language.

They say “similar to Markdown” because that’s the best-known lightweight markup language, so it’s the obvious reference point.