Burned and burnt are both correct past forms of the verb burn. In American English, burned is the usual past tense and past participle, and burnt is mostly used as an adjective, as in burnt toast. In British, Australian, and Irish English, both forms are common for the verb as well.
English has many words that cause confusion. Some sound alike but mean different things, like principle and principal. Such words are called homonyms, homophones, or homographs, depending on whether they share their sound, their spelling, or both. Burned and burnt are a different case. They are two forms of the same word, like learned and learnt, spelled and spelt, or dreamed and dreamt. So what is the difference between them, and which one should you use?
Where you live makes the difference
Which form you use often depends on where you live. People in Britain, Australia, and Ireland tend to use both words interchangeably as the past tense of burn: to them, they are the same word. In the United States and Canada, writers generally use burned for the verb and keep burnt for the adjective.
I was shocked to see the entire forest burnt to the ground.
No one wanted to eat the burnt turkey.
Is there a reason why the house burnt down?
All 3 sentences are correct. In the first and the third, burnt is a verb, so a writer in the United States or Canada would most likely write burned there. In the second, burnt is an adjective that describes the turkey, which is common in American English too.
Verb or adjective?
In American English, burnt is usually an adjective. It describes something that has been burned: burnt toast, a burnt smell, burnt sugar. Burned is the verb form. It tells you that something burned, or was burned, in the past. Both words can serve as the past tense and the past participle of burn, but they are used differently.
Two forms, two traditions
Both forms have been in use for centuries. British English kept both of them, while North American English settled on burned for the verb. Today burnt as a verb is mainly found outside North America, and to many American readers it sounds British or old-fashioned.
So a person in Britain may say either of these:
My sister burnt the toast.
My sister burned the toast.
A person in the United States would most likely say the second. Both of them, though, would probably call the result burnt toast.
A tip to remember it
There is an easy way to remember which word is used where. Think of the letter T: it is in burnt, and it is in Britain. Link burnt with Britain, and you will remember that burnt as a verb is common in British English and much less common in North America.
If you write for American readers, use burned for the verb and burnt for the adjective. Whichever you choose, stay consistent. The guide to British or American English shows how to keep one variety of English from the first line of a text to the last.