Jobs in both fields can be incredibly variable because the fields are just so diverse.
For a start though it's now what people associate with it! A lot of people think marine biology=marine mammals; dolphins, whales, seals...
This is a misnomer, it's not actually like that. A few marine biologists do study marine mammals but that is a tiny minority. The same way zoology does not neccessarily mean working with primates, big cats or wolves.
Let's start with marine biology, what exactly you end up doing once you have your degree depends heavily on the field you choose.
You could spend the day processing water samples in the lab and counting algal cells under a microscope (for example if you study red tide), you could be analysing tissue samples to find out contaminant levels in different species of marine animals, you could be teaching at a university, you could be patrolling beaches for sea turtle nests, you could be cleaning out aquarium tanks, you could be involved in an environmental impact assessment, you could be devising a new plan to protect coastal communities, you could be writing grant proposals and meeting with potential sponsors, you could be on the computer doing research and reading up on papers relevant to your own research, you could be statistically analysing your data and writing up the results, you could be on the shore measuring algae fronds or setting up quadrants to study inter-tidal communities, you could be on the beach digging holes to obtain samples from deeper layers to assess the population of interstitial microfauna, you could be taking blood from crabs to determine hormone levels, you could be out on the boat doing research and experiments; for example fishing and evaluating the catch, or taking plankton samples- in short there is a lot of things you could be doing, from complete desk jobs to research jobs out at sea.
It should be noted however that desk jobs usually greaty outweigh actual field and research jobs and it may not be able to always 'choose' what you want to do, you can work to go into a certain direction but you may need to make compromises and work some jobs you are not too keen on in order to get to those you really want. Marine biology jobs are highly competitive so if you get considered for one it would be a bad idea to turn it down!
Zoology is equally variabe, strictly speaking it is of course the study of living organisms however there are a lot of different aspects you could be looking at:
1. Comparative anatomy studies the structure of animals.
2. The physiology of animals is studied under various fields including anatomy and embryology
3. The common genetic and developmental mechanisms of animals and plants is studied in molecular biology, molecular genetics and developmental biology
4. Ethology is the study of animal behavior.
5. The ecology of animals is covered under behavioral ecology and other fields
6. Evolutionary biology of both animals and plants is considered in the articles on evolution, population genetics, heredity, variation, Mendelism, reproduction.
7. Systematics, cladistics, phylogenetics, phylogeography, biogeography and taxonomy classify and group species via common descent and regional associations.
8. The various taxonomically-oriented disciplines such as mammalogy, herpetology, ornithology identify and classify species, and study the structures and mechanisms specific to those groups. Entomology is the study of insects, by far the largest group of animals.
In general for both jobs, if you want to get into research, it is advisable to take it to at least the MSc. level. You can get some jobs with BSc. level but if you're aiming to do your own research, it is advisable to get at least a Masters. Of course that does not mean you will get a research project straight out of uni, mostly you will have to do other people's research for a while but the chances are improved if you do have a Masters.