This article is posted from me with a kbin account, on a kbin magazine:-). The true beauty of the fediverse is that you need not care - like if I had a gmail account and you had a yahoo one, you could still receive the message despite being on entirely different servers.
Various Lemmy instances are part of the fediverse, and run the Lemmy code (various scripting languages - Rust, Actic, Diesel, Infero & Typescript). Each admin can do whatever, like modify the sourcecode, mess with their personal databases, etc., which can lead to different Lemmy instances using different versions of the sourcecode, which happened a few weeks ago and led to problems connecting when a new version became incompatible with the old.
Kbin is not a Lemmy instance though - it is a completely different implementation built from the ground up, in PHP & PostgreSQL - but it still uses ActivityPub so it can share with Lemmy the same as any Lemmy instance could. Meta (Facebook) will similarly implement ActivityPub in some manner and so also be able to communicate across the Fediverse. (Also as people are saying, Kbin also has implementation to share with Mastodon too while the Lemmy code does not.)
Unless an individual Lemmy - or a Kbin - instance wants that to not happen, i.e. to defederate, which is a whole other matter.
So:
instance = a particular machine (lemmy.ml or lemmy.world or beehaw or whatever);
Lemmy = code, or Kbin = different code, running on that instance, affecting what/how/etc.;
fediverse = everything that shares messages, like if one day a decade from now Reddit (may the spez have been fucked over MANY times before that day:-P) was forced to adopt ActivityPub and become a member in order to stay relevant, then it would become a part of it as well;
defederate = a specific blocking of messages from one instance to another (not necessary 2-way)
So if you thought of yourself as a Lemming/Lemmon/whatever before reading this comment, it is probably better to start thinking of yourself in terms of being a fedizen now - a member of the wider fediverse. You always were, you just did not know that yet:-).