A consistent terminology for quantifying species diversity? Yes, it does exist.

The prevailing terminological confusion around the concept 'diversity' has hampered accurate communication and caused diversity issues to appear unnecessarily complicated. In fact, a consistent terminology for phenomena related to (species) diversity is already available. When this terminology is adhered to, diversity emerges as an easily understood concept. It is important to differentiate between diversity itself and a diversity index: an index of something is just a surrogate for the thing itself. The conceptual problem of defining diversity also has to be separated from the practical problem of deciding how to adequately quantify diversity for a community of interest. In practice, diversity can be quantified for any dataset where units of observation (such as individuals) have been classified into types (such as species). All that needs to be known is what proportion of the observed units belong to a type of mean abundance. Diversity equals the inverse of this mean, and it quantifies the effective number of the types of interest. In ecology, interest often (but not always) focuses on species diversity. If the dataset consists of (or gets divided into) subunits, then the total effective number of species (gamma diversity) can be partitioned into the effective number of compositionally distinct subunits (beta diversity) and the mean effective number of species per such subunit (alpha diversity). Species richness is related to species diversity, but they are not the same thing; richness does not take the proportional abundances into account and is therefore the actual-rather than the effective-number of types. Most of the phenomena that have been called 'beta diversity' in the past do not quantify an effective number of types, so they should be referred to by names other than 'diversity' (for example, species turnover or differentiation).