Elite is a name Kenmore decided to give to a line of it's appliances - like KitchenAid uses Artisan and Professional to distinguish between different models of their stand mixers.
I have never seen a "gas" cooktop that had a perfectly flat glass surface like electric (induction/conduction/infrared) models. And, the only time I have seen the terms ceramic/enamel/ceramic enamel used for a gas stove/stovetop refers to the bonding of a ceramic enamel to the surface of the metal - similar to the process LeCreuset (for one example) uses to bond ceramic/enamel to their cast iron and carbon steel pots-n-pans.
A "drop-in" cooktop is one where you have a cutout opening in a flat countertop surface and the cooktop "drops" into the hole - the surface of the cooktop is generally almost flush with the countertop (with the bottom of the unit extending into the cabinet space below) - with the burners and knobs being a little higher than the counter surface, naturally. You can compare this to a kitchen sink where they cut an opening in the counter for the sink and then "drop" it in.
My best suggestion would be to find out where your girlfriend got hers and start there. Some stores, like Sears/Montgomery Wards/RadioShack I know for sure, have things in their in-store catalog that they do not have on the web sites.