Classification is a very broad term which simply means putting things in classes. Any kind of organisational scheme is a classification: for example, sorting smarties by colour, coins by diameter or cities by population. Humans seem unable to resist the urge to classify. It is one of the most basic activities of any science, because it is easier to think about a few groups of things than about lots of separate things.

Taxonomy means giving names to things. It tends to go hand in hand with classification, but need not. You can arrange things without naming them, or name them without arranging them, but the most helpful schemes name things in a way the reflects their classification.

It is the basis of classification that decides the taxonomy of an entity.