>>11712152It can be misleading to think of large cardinal properties corresponding to big cardinals. For instance it is consistent with ZF that is a measurable cardinal, and is a the smallest uncountable cardinal. A better intuition is that a large cardinal property is the assertion that a certain cardinal has a property, like being measurable, Ramsey or whatever. In fact, not everything mentioned on that list is even a cardinal, for instance can be thought of a set of natural numbers that code a model of set theory. Most large cardinal properties assert the existence of elementary embedding of the universe into some class. The question mark you have at the top is 0=1, since everything is consistent (as well as inconsistent) with that assumption. That figure is from Kanamori's book Higher Infinite.
