I am looking for an apartment to rent. There is one that the agent said has no oven but only something I didn't catch from her speaking. I usually call those round things on the top heated by either cooking gas or electricity, "stove" or "range". But I am not an native American English speaker. So I wonder if cooktop, range and stove all refer to those round things on the top? What differences are between them? Thanks!
Yes, the cooktop is the top part of a stove (also known as a range) - just the burners/heating elements (the round things you refer to), which as you've discovered can be found without the oven underneath! There's not really a difference beyond that. You can see this pretty easily if you google "cooktop" and look at the pictures of the products you find.