Good definitions are crucial for most research studies, especially in literature reviews, where topics and concepts must be precisely specified. Attempts to guide scholars in developing clear definitions have mainly emphasised necessary and sufficient definitions (also called intensional definitions) that strictly define things using a minimal set of required terms. Family resemblance concepts have also been suggested when attributes or features are optional. However, many definitions sometimes require complex combinations of some required and some optional terms, which are not adequately addressed by either type of definition. Thus, drawing from formal axiology, we develop two new useful types of definition: differential definitions to specify the minimal reducible notion of what a thing is, including complex term combination logic; and expositional definitions to specify what a thing might optionally be. These types are more flexible and yet precise in specifying the meanings of terms.