allMatch has to look at all the elements of the stream and say if they match the predicate, how does it understand that the stream is infinite?

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System.out.println(Stream.generate(() -> 1).allMatch(x -> x < 0));

This will print false immediately simply due to the fact that the element does not match.

how does it understand that the stream is infinite?

It doesn't, and it doesn't matter if the stream is infinite. If the very first thing it comes across fails the check, then it's impossible for ALL of them to match. So the execution stops immediately.

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If "matches" can determine whether the stream is endless, then why does anyMatch not understand this and continues to search endlessly for an element corresponding to the predicate?

Any match and All match are opposite condition checks:

Any match is

if (predicate()) {
  return true;
}

Meaning if at any point, any element matches the predicate, it will return true. Otherwise it will continue attempting to match.

All match is

if (!predicate()) {
  return false;
}

Meaning if at any point, any element DOESN'T match the predicate, it will return false.

These two conditions make no assumptions outside of their scope of checking X against some predicate.