I'm a US native speaker. I would describe it this way: "This is an electric stove with four burners. The part of the burner that gets hot is the heating element. The stove is designed so that you can remove the heating element easily to clean underneath it."
A brand name for a common kind of heating element is "Calrod" and I have sometimes heard heating elements referred to as "calrods."
To me, a "hotplate" is a small portable electric device with either one or two burners. For example, "Because of safety issues, hotplates are strictly forbidden in the student dormitory."