Presuppositions to Minds, Thoughts, and Things
Perhaps one of the simplest metaphysical views one can take is the notion that the apparent dichotomy of mind and body is essentially the nature of reality itself, with the mind and thoughts being in some form of direct contact with the environment and things in it. This is known as naive realism, and is often the starting point for a person's experience as they grow philosophically. It rests on some metaphysical musings on the nature of extension and intension (which are not opposites). That is to say, we seem to be intuitively aware of space outside and that we have meaningful ideas related to words and their meanings. Obviously, as one engages in philosophy, things get complicated fast.
'Ontology' is the study of things, and since we study things, it is appropriate to ask if things are real and objective only, or are they also what goes on in our minds. Hence, are our thoughts things? Well, if one needs a convenient way to express the difference between things of the mind and things of the physical world, then maybe it's best to reserve 'things' for the physical only. But if we do that, how do we generally refer to entities of the mind? Thoughts? Beliefs? This question of generalizing between physical and mental creates three questions regarding generalizing: what to call things of the mind, things of the physical world, and to call things that are either of the mind or the physical world. One good candidate for a generalization of all ontological primitives might be 'object'. From the SEP article:
One might well wonder—is there a category under which everything falls? Offering an informative account of such a category is no easy task. For nothing would distinguish things that fall under it from those that don’t—there being, after all, none of the latter. It seems hard, then, to say much about any fully general category; and it would appear to do no carving or categorizing or dividing at all. Nonetheless, there are candidates for such a fully general office, including thing, being, entity, item, existent, and—especially—object.2
Objects, Terms, and So On
First, note that this object isn't the same object of the subject/object dichotomy, although one might see the dichotomy between the external and internal at play in a sentence like "I see a dog". The use of object as the most general class might be seen as the most general category or linguistic classification of ideas from a phenomenological perspective. There hasn't been a universal consensus on terminology in this regard, and so philosophers tend to provide definitions to clarify in their work. Many philosophers have had their own preferred term that denotes essentially what is meant herein by 'object'. Russell was fond of 'term':
I shall use as synonymous with [‘term’] the words unit, individual and entity. The first two emphasize the fact that every term is one, while the third is derived from the fact that every term has being, i.e. is in some sense. A man, a moment, a number, a class, a relation, a chimera, or anything else that can be mentioned, is sure to be a term (1903: 43)
One ontologist to develop a theory of objects is the Austrian ontologist Alexius Meinong.
According to the Encyclopedia of Philosophy, the Theory of Objects has two basic theses:
(1) [T]here are objects that do not exist and (2) every object that does not exist is yet constituted in some way or other and thus may be made the subject of true predication. Traditional metaphysics treats of objects that exist as well as of those that merely subsist... but, have "a prejudice in favor of the real," tends to neglect those objects that have no kind of being at all; hence, according to Meinong, there is need for a more general theory of objects.
So, here we see an effort to rigorously answer your question. What is Meinong's taxonomy of all objects in the world? Does he favor internal/external, real/imaginnary, so on? From WP's article on Meinong:
Meinong distinguishes four classes of "objects":
"Object" (Objekt), which can be real (like horses) or ideal (like the concepts of difference, identity, etc.)
"Objective" (Objectiv), e.g. the affirmation of the being (Sein) or non-being (Nichtsein), of a being-such (Sosein), or a being-with (Mitsein) - parallel to existential, categorical and hypothetical judgements. Objectives are close to what contemporary philosophers call states of affairs (where these may be actual—may "obtain"—or not).
"Dignitative", e.g. the true, the good, the beautiful
"Desiderative", e.g. duties, ends, etc.
It's tempting to think that metaphysics and metaphysicians are a monolithic entity with a set of theoretical and precising definitions in the same way that physicists or computer scientists have, but the truth is even in the analytical philosophical tradition such an effort such as those of experimental philosophers might be viewed as an inchoate program, so no such consensus exists. On the upside, that leaves you free to be the next great epistemologist to take the work of Quine's naturalized epistemology to the next level. If you prefer to use 'object' to denote real things and mental abstractions, you wouldn't be alone, but the same could be said if you attempted to cook up your own ontology.