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Ontology is a house within philosophy's major branch metaphysics, which is theory of reality. Although metaphysics overall discusses the nature of and relations among things that exist, ontology—occurring within metaphysics—first postulates the categories of being, simply what exists. Ontology establishes categories.
Ontology is part of metaphysics since in philosophy's major branch epistemology—which concerns the sources, nature, justification, scope, and limits of knowledge, which is justified and not just incidentally correct belief—it is generally accepted as impossible to justify that the manner whereby one recognizes things and sorts them by identified traits is truly the only natural way to do so.
Coherence and correspondence
Depending on one's theory of reality, which can be either realist or idealist, one can seek either a correspondence theory of truth or a coherence theory of truth. A realist metaphysics frames statements to correspond to a reality presumed to exist independently of the mind. An idealist metaphysics frames statements to cohere with other statements, as it recognizes no mind-independent reality to exist, or, even if it presumes one to exist, regards that mind-independent reality as unknowable. So a realist ontology can seek correspondence as well as coherence, yet insofar as realism, it uses coherence to aim for correspondence. An idealist ontology can claim only to aim for coherence with other statements or perceptions of minds.
The term ontology can refer to a statement's ontological setup even if the statement's speaker is not intending metaphysics. A speaker's ontological and thus metaphysical commitment or presumption is reflected in the speaker's framing of what exists—naturally or mentally or both—and how such existent thing is sorted into its presumed category. For instance, life can be ontologically posed as either God's grace or as soul or as vital force or as functioning organism or as molecular illusion or as ubiquitous substance.