It seems to depend a little on context, from what I've experienced (which is being introduced to an entire sprawling family by being referred to with 'fidanzata'). 'Fidanzato/-a' is commonly used to refer to a partner you're a little more serious about than 'just' someone you're dating, without necessarily being engaged to them. Interestingly enough, the concepts are also often confused by Italians speaking English as a foreign language --sometimes they'll say 'fiancé(e)' when they're not actually engaged with their partner.
Don't forget we are learning ITALIAN, so the irritation of being held to some mid-Atlantic English standard tends to have aspects of two bald men arguing over a comb. Hold to tight standards for Italian by all means, but cut some slack with English. Remember which language we are learning.
In French the word is fiancé for a man and fiancée for a woman. The acute accent (é) changes the pronunciation of the letter E. Having borrowed the word into English we can leave off the accents (especially from the feminine word) since they don't really mean anything to us, but if you do use them they should be acute (rising from left to right). Hope that helps!