Answer from "Marsh Maven", a Marine Biologist:
That is a very good question, and not always easy to find an answer. Many people use them interchangeably.

Oceanographers study how oceans work, and there are many different types of oceanographers. They often make measurements at sea, conduct laboratory experiments and make models. Physical oceanographers study water masses and currents in the oceans and interactions of different energy forms (such as light, heat, sounds, wind, etc.) in the ocean. Chemical oceanographers look at the distribution of chemical compounds and the interactions that occur in and between the air, ocean and seafloor. Biological oceanographers describe life forms in the sea with their natural environment- describing their population patterns and how plants and animals interact with each other, inorganic substances and energy sources. Geological oceanographers describe the seafloor and things like sediment transport in currents. They can also be ocean engineers and technicians.

Marine Biologists study the living resources in the oceans and seas and ask questions specifically about ocean life. They look at interactions among species, ecosystems, or between the organisms and its environment. They take samples at sea or conduct experiments either in the ocean or in the laboratory. The marine biologist is similar to the biological oceanographer in many ways.

There is an interesting website that answers many questions related to marine biology and oceanography that can be found at the following web address: http://scilib.ucsd.edu/sio/guide/career.html Check it out!

Thanks to Terianne from Winter Hill Middle School for submitting this question!