Classification is a system of putting things into a separate niche, or category that represents that one thing only. I will present this answer in terms of living organisms, so when an organism is classified, it is because it has a certain set of physical characteristics that describe that organism only. Classification can get quite complex, when you think about all the different living organisms on Earth. This is where the term diverse comes in. Diversity is a more general concept, employed to describe an ecosystems flora and fauna in terms of scarceness, where only a few forms exist, moderate, where an acceptable number exist, or rich, where abundant numbers or organisms exist. When thinking about the biomes, it is interesting to note the polar extremes, where life forms are scarce, to the tropical extremes, where the greatest diversity is found in both plants and animals. So, a good way to look at this is the difference between talking about one specific organism and talking about lots of different organisms.
diversity is The number and variety of species present in an area and their spatial distribution while Classification, or taxonomy, is a system of categorizing living things. There are seven divisions in the system: (1) Kingdom; (2) Phylum or Division; (3) Class; (4) Order; (5) Family; (6) Genus; (7) Species.