Valid question. The dictionary narrows the definition of pūlehu this way: "To, broil as sweet potatoes, breadfruit or bananas placed on hot embers." So,broiling can mean direct, intense, radiant heat. The same dictionary describes "broil" as "pūlehu (on coals); lāwalu (in leaves); alehu, kō'ala, kunu, 'ōlani, pālaha, 'ōhinu, pāki'i." (Whew.) In my kitchen, I broil under a heating element. I think Duolingo doesn't use pūlehu and kō'ala interchangeably, though. While the pūlehu deals with cooking veggies, kō'ala deals with cooking meat. And that's the difference between the two--at least, as far as I can make out.
Okay so what's the difference between broiled and baked? The heating elements are below the cooking rack in the oven as well. The dropdown definition gives both "broiled" and "roasted" for "pūlehu," (so it wouldn't have helped even if I'd checked that before hitting "check"). Is there a difference there? Isn't "roasted" something that happens inside an oven? (Learning vocabulary in another language is so much more difficult when you're unsure about the definitions in your native language. And clearly, I'm not a cook either!)
I cannot seem to relate the American English to Hawaiian, so for the sake of the exercise, I am going to try this.
Puhi is to bake, which is what you do for breads and cakes.
Pūlehu is a type of grilling, mostly for vegetables.
Ko'ala is a type of grilling, mostly for meats.
It has less to do with the fire technique and more to do with what is being cooked. If the oven is in the ground, then it is kālua.
I think DL is pretty consistent along those lines.
OMG Bless your heart!! Mahalo nui for the mnemonic and visuals you put in my head with your descriptions. Here's hoping my antique brain can absorb them - I don't care what the words are in English as long as I can figure out which of these is being described. Puhi for baking cakes Pulehu for veggies (happy turkey) Ko`ala for meats Kālua requires an imu. Got it! Mahalo nui loa - you my hero!