Standard English, as spoken in North America:
major appliances - ovens, stoves, washing machines, dryers, washer/dryers, freezers, refrigerators
white goods - until the 1950s, mass-produced "modern" appliances were almost always painted white, so people called them white goods.
1. cooking zone - a place on a cooking surface which is often round or oblong, and onto which pots and pans are placed for heating, sauteeing, pan frying, and the like
2. burner - a cooking zone which provides direct heat, and is usually round. This term would not apply well to induction "burners", since they don't provide direct heat
3. eye - a cooking zone which is usually round.
4. coils - a cooking zone which employs electric coils.
5. cooktop or stovetop - a flat surface which is usually rectangular and which usually has at least four cooking zones. Typically, there will be one of the following combinations: four electric coil burners, four or five open gas burners, four or five sealed gas burners, four or five glass-ceramic areas with gas burners underneath each, four or five wood burners (especially on old or old-fashioned cast iron stoves), or four or five induction cooking zones.
6. oven - an appliance with an open cavity into which bakeware and cookware (but usually not pans) are placed. The appliance may include a cooking surface, such as a cooktop.
7. standalone oven - an oven which does not include a cooking surface
8. wall oven - an standalone oven which is built into a wall
9. stove - a cooking surface, an oven, or a heater
10. range - a cooking surface or an oven
11. hob - not in usage, but it is likely to be understood to mean "cooking surface" or "cooktop"
12. cooker - not in wide usage, but it is likely to be understood as a small appliance, rather than a major appliance