“What a thing is” and “that a thing is” refer to a thing’s essence and existence. The “what” is its essence; the “that” is its existence.
Consider the case of the Sasquatch. For generations, people have claimed to have caught glimpses of this half-man, half-ape like creature lurking about in the forests of Canada. “What is it?” someone asks of the beast; “what does it look like? What does it eat?” This line of questioning is focussing on the creature’s essence, its traits. What makes a Sasquatch different from a big ape? When we establish what a thing is, we are establishing its essence.
But notice that in establishing a things essence we are not establishing its existence. You could become a world expert in the nature of the Sasquatch: where the legend originated; what height it is supposed to grow to; what it would likely eat; how many people have claimed to have seen it; that is is smelly; that it has big, dirty toenails; what parts of Canada it is likely to inhabit. But all this information about its essence doesn’t bring us any closer to the question: “Does the Sasquatch exist?” It may or may not exist, but knowing lots of stuff about its essence does not help us answer questions about its existence. It may be more likely that it does not exist. Or perhaps we will all be surprised and excited one day to find that such a creature has indeed been shot and bagged.
So we can say that essence and existence are two distinct things. “What a thing is” and “that a thing is” are not the same thing: at least in reference to the Sasquatch and—for that matter—all creatures, real or not.
But notice how this separation of essence (“whatness”) and existence (“thatness”) does not apply to everything. It does not, for starters, apply to the sum, 3 + 5 = 8. What the sum is and its existence cannot be separated. In essence, it is a sum. Specifically, its essence is the sum of 3 + 5. Does it make sense to say that this sum might not exist? The fact that we understand it’s essence implies that there is something we understand. There must be something that exists in order to be understood.
Of course, the sum does not exist in the same way that donkeys and cabbages exist. It has a purely conceptual existence: it exists in the mind. But to know its essence is the same thing as knowing its existence.
So there are things for which essence and existence are different as in the case of Sasquatch, lasagne, the Prime Minister and cornflakes. And there are also things for which essence and existence are the same as for sums and ideas.
Anything in which existence and essence are not the same are called contingent things. It is possible that they do not exist; and if they do exist, it is possible that they can go out of existence. On the other hand, things in which existence and essence are the same or occur together are necessary. They are necessary because the fact of their existence cannot be separated from the fact of their essences. You cannot say that 3 + 5 is a sum which equals 8, and then deny that there is such a sum.