Yes, the two extremes are captured by the common metrics of "species richness" which is the pure "how many unique species are there", and "species evenness", which depends on how evenly distributed the species are. A community in which 99% of individuals are species A and the remaining 1% are from species B-G is exactly as species rich as a community in which there are equal numbers of individuals of each species, but it is much less even (and therefore, under one extreme of diversity, less diverse). In different contexts and for different ecological questions, these two different versions of diversity can matter more or less, and there are metrics which take both into account, but this is a fully generalized solution which shows you relative diversity along the entire spectrum from "all I care about is richness" to "all I care about is evenness".
-edit- by the way, since it may not be obvious to everyone, the reason why an ecologist might care bout evenness is because extremely rare species are often not very important to the wider community. From an ecological function perspective, there is very little difference between my above example of the 99%/1% community and a community that is 100% species A. So an community with two, equally populous species might have more functional diversity than a community with one very abundant species and several more, very rare species.
-edit- by the way, since it may not be obvious to everyone, the reason why an ecologist might care bout evenness is because extremely rare species are often not very important to the wider community. From an ecological function perspective, there is very little difference between my above example of the 99%/1% community and a community that is 100% species A. So an community with two, equally populous species might have more functional diversity than a community with one very abundant species and several more, very rare species.