The usage of grill here is British English, not American.
From the Oxford English Dictionary:
1 A device on a cooker that radiates heat downwards for cooking food: place under a hot grill [as modifier]: a grill pan
This is a modern domestic cooker, specifically a Neptune 4500 combination gas oven, burner and grill:
This part is the grill pan.
Here is the actual hot grill (not the same model of cooker - this one is inside an Electrolux electic fan oven). An electric heating element at the top inside the upper compartment. Occasionally it may use gas flames instead.
You put food on the pan and place it under the grill. If the control knob is in the low position then the element will not be that hot. In which case whatever food is under the grill will be cooked slowly.
In all British kitchen appliances this device is called the grill or grill element, and in all recipes the use of this device to cook food is called grilling.