There are variations between all organisms on the planet - the differences between species are obvious; sometimes the variation within a species is less marked. All organisms of the same species are similar because they have the same genes. The variations occur because of the different alleles (different versions of the same gene e.g. blood type has A, B and O alleles) present.
Adaptations are characteristics that aid an organism’s survival. Because the characteristics within a population vary, this means that some individuals are better adapted for survival. It is the combination of different alleles that an organism has that leads to these adaptations.
Evolution is a gradual change in the characteristics of a population over a long period of time. The process which drives evolution is natural selection. The theory of evolution by natural select says that because all organisms of the same species are competing for the same resources, those that are better adapted are more likely to survive and reproduce. This means that the alleles that code for those adaptations will be passed on, and so over time the whole population changes to have those alleles. This cycle is continuous, with different adaptations being better suited to an ever-changing environment.
Classification is a way of sorting organisms into different groups to make them easier to study. There have been many different ways of classifying animals - based on appearance (older systems), DNA, biological molecules present in the body, embryonic development etc. The system starts with large groups, and then splits to form smaller ones - there are more groups at each level of organisation but with fewer organisms in each.
Because the system is hierarchical (split into levels), each organism is known only by the last two names - the genus and the species. In the example shown, Canis familiaris is the dog.