One finds the word "ontology" referred to quite frequently. So frequently, in fact, and in such varied and disparate ways, that poor wanderers through the vast halls of intellectual history such as your charming and delightful old Uncle Ciceronianus find it hard to determine just what it is, and indeed whether it is anything at all.
Ontology you must understand is no longer the concern merely of philosophers, which would of course make it of no concern to most. The word, at least, is thrown about in discussions of all kinds, as carelessly as one might throw a Nerf Ball, secure in the knowledge that nothing of significance will result or subject one to blame.
If we gather our strength enough to consult a dictionary, we'll find that "ontology" is said to be a branch of metaphysics concerned with the nature or relations of being, or a theory regarding the nature of being or the kinds of things that have existence. If you're anything like me, this definition raises all kinds of questions, but none which have to do with the apparent subject matter of ontology. Instead, those questions would involve whether anybody actually devotes time to the study of ontology, and if so why they do.
If the nature of being refers to the nature of existence, we all seem to have some idea of the fact that we exist, and may even be said to know we exist. No great effort is involved in arriving at these conclusions. We may indulge in faux doubt as did Descartes, but that is futile and tiresome. We may indulge in the same kind of doubt as to the existence of other people and things if we really want, but nobody does that sort of thing in fact, i.e. we do what we need to do to live and living involves interaction with other things and people; if conduct is any kind of guide to what we in fact think, it's silly to maintain we think they don't exist.
Are there (still) people who seriously wonder whether they exist, or whether other creatures or things exist? Perhaps there are, but if so I question whether there are enough of them to make "ontology" the kind of buzz word it seems to be. Are there people who seriously ponder what it is for them or other creatures or things to exist? It's likely there are more of such folk than there are those who seriously wonder whether they or others exist, but think that if they ponder this "question" in the abstract, without addressing it in a particular context or set of circumstances, their habitat is the university, i.e. the academy.
What it means for us to exist, or for other things to exist, may be something which presents questions which actually require or may result in answers in certain circumstances. We may have reason to describe what is taking place and what we do in interacting with other things and people, which may be said, speaking rather awkwardly and in a contrived fashion, to relate to the nature of our/their existence or being. Even then their being/existence isn't an issue. But to refer to being as an attribute of all things and define just what that attribute is as to all things and in isolation (without addressing a particular situation) clearly isn't something we do or would seem to have reason to do in ordinary circumstances. Nor does it seem there is any reason to inquire what it is for anything to be, though it may be something we do when drunk or high or in a philosophy class.
We say something exists, has being, when it's present in time and space. We consider or recognize the characteristics of what is present in time and space when we interact with it, which we may do for various reasons, or when we encounter it, interact with it. Sometimes we do that for a reason or for a particular purpose, sometimes we don't (we may, for example, bump into something accidently). But existence isn't an issue unless whether something exists is unknown and it's important in some manner to know if it does or does not. Ontology won't answer this question, however. I don't think it's intended to answer it.
We may, if we really want to, engage in the study of what it is for anything to exist, unconnected with any circumstance or context, what "being" is, but in doing so I don't think we can do more than say, e.g., that it must have substance, be part of the universe, not be something which only one person can see, touch, etc.; in other words, we would only come to conclusions which are obvious and trivial, which achieve nothing.
So I think that what is referred to as ontology or ontological so often these days has nothing to do with "being." The existence of something or some person isn't being studied or analyzed, in and of itself. That existence, or being, is taken for granted. What we are doing in fact is ascertaining the characteristics of something we know has being, determining how we should or can interact with it, generally for a particular purpose. Our concerns may be practical, scientific, instrumental, economic, religious or otherwise, but our concern is not being, not our being or that of any other thing or creature. Instead, we accept being and concern ourselves with the consequences of being.
Why we choose to call this ontology, or describe it as the study of being, I can't say. I'm reasonably certain, though, that we gain nothing by doing so, and have concerns that in doing so we merely render obscure matters which may usefully be considered if only we refrain from indulging in what Dewey liked to call "The Philosophical Fallacy"; roughly speaking, the neglect of context.