Oxidation states are a measure of the difference in the number of protons and electrons in an ion or atom
The transition metals is a term given to the group of metals that occupy the centre of the periodic table. They are known as the transition elements as they bridge the gap between group 2 and 3. They are all metals, form coloured compounds and can act as catalysts with variable oxidation states.
The lanthanides are a series of chemicals in the expanded periodic table that have an expanded number of orbitals beyond that of the transition metals. The lanthanides are mostly soft metals with their hardness increasing across the period. Whilst they are metals and can conduct electricity the lanthanides have a relatively high resistivity.