Amazon was rebranded LeetCode for their "entrance level". FB was writing code in what appeared to be more Microsoft Word-like. (There was no console to check my work). But the conversations with actual humans was where things diverged. The systems design stuff for Amazon was very "we're looking to zing you". Facebook was definitely "hmmm, that's an interesting approach, have you considered....?" or "That sounds like it would work but, what if we...." That type of interviewing really makes one feel like they're part of a team instead of being completely alone. Amazon seemed to thrive on the "you're scared, alone, and you need to build a bloom filter and figure out an efficient hashing algorithm NOW." I realize this is probably not everyone's experience. I am not saying "Amazon sucks, all their interviews are bad" I was simply sharing my experience as it's what led me to remove my candidacy.
AMZN's was very pleasant, though I think because I was a referral, I was side channeled and would have gone through their normal unpleasant process eventually if it was a good fit (it wasn't).
My FB interview was very similar to your AMZN description. They gave me a CS interview guide, told me to spend a few weeks studying it, and did the algorithm lottery on me. The main reason I declined to move forward was because they couldn't guarantee I'd actually get the role I was referred into and basically none of the process was role-relavant. It felt indistinguishable from the AMZN tech interview.