Oxidoreductases are the enzymes which catalyze biological oxidations and reductions- the removal or addition of hydrogen atoms. Dehydrogenases, oxidases (where oxygen acts as acceptor) and oxygenases (where oxygen is partly incorporated into the molecule), and peroxidases are the trivial names of the many enzymes found in this class of enzymes.
Malic dehydrogenase would be given the systematic name of malate-oxidoreductase. A dehydrogenase or reductase is an enzyme that catalyzes the dehydrogenation or removal of hydrogen atoms from one substrate A, transferring them to another substrate B (other than to molecular oxygen. An oxidase is an enzyme that catalyzes the transfer of hydrogen atoms from a substrate.