A cooker is an oven basically. In British English, we call the electric or gas rings on the top 'the hob' and the compartment underneath is the oven. The whole thing is a cooker.

In my understanding, the term "cooker" in British English indeed refers to a cooking appliance, similar to what might be called a "range" or "stove" in American English. This appliance typically includes both an oven and stovetop burners on top. So, while "cooker" doesn't mean "oven" exclusively, it encompasses the oven as part of the whole appliance. The context of the British English listening exercise might have used "cooker" in a way that emphasized the oven function, which could explain why it seemed to specifically refer to an oven. This distinction in terminology between British and American English can indeed be a bit confusing at first.

So yes, Lucy, it should be "oven."

You need to check four or more dictionaries to get a full understanding. The two words oven and cooker can both be exactly the same thing. And they can also for many complex historically and etymological reasons be referring to two completely different things. Also the word stove can be placed in this category and can be used to mean the same thing or a different third thing. The technical differences come into play in the commercial, industrial and scientific environments. Example a stove is an oven or a cooker it is a container that is heated up and you can cook in it on it by placing food water etc on top of it. But a stove can also be only a heater if it is built in a certain way. You would not normally use an oven or cooker specifically to heat a room. https://dictionary.cambridge.org/dictionary/english/stove An oven is the enclosed part of a cooker with a door on it to enclosed the food being cooked. Or in scientific or industrial purposes for drying paint onto metals or for a ring process etc. the list is endless. A cooker is often nowadays a multi purpose piece of equipment that has an oven below for cooking and roasting etc, above are hobs or gas and electric rings hotplates etc. It is therefore a full cooking appliance. IN NORMAL EVERYDAY SPEAKING Oven and cooker and stove are considered the same and if you look online at shopping sites and catalogues you will see all three oven, cooker and stove all showing the same pictures. IN THE CONTEXT OF THE WRITTEN TEXT ABOUT COOKING ! Yes they are all the same. Because you can buy ovens that are only ovens --> this is where we get the term "microwave oven" --> there is no cooking possible on top of a "micro wave oven" Also we do not see a picture nor a description of the oven in the text.

yes, it's "oven" because "bake a cake", may mean "stove" in general