The word 'desirable' I find is a little harder to explain. Not only can people be desirable, but objects and situations. Personally I wouldn't call someone that I think is charming desirable to their face, since that can sometimes feel a little demeaning, like that are an object that many people want. When you say someone is desirable it means that you think they hold the qualities and looks that are preferable to you, so its not always necessarily a compliment to them. Common examples of this word can include: A famous celebrity, many people could say she/he is very desirable due to their looks and fame. Sunny weather would be most desirable for tomorrow That is explaining the best possible situation he/she could want to occur Millions desire to own their own home one day This explains a common ideal that many have and wish for The gold watch was the most desirable item in the auction. This means that, out of all the items for sale, the gold watch was the item that most people wanted, due to looks, material, rarity, etc

The words attractive and desirable do hold similar meaning however they should not be used interchangeably. If you wanted to pay a compliment to someone you have just met or do not know too well, though you think they are charming, these words in my opinion are a bit too strong to use and would not be appropriate, since they could think that you are trying to pursue a relationship, though in a very forward way. You would generally use the word 'attractive' towards someone who you have a romantic relationship with or you and that said person are pursuing such a relationship, e.g.: girlfriends/boyfriend. "I think you look really attractive in that outfit", "Im really attracted to you". There are some exceptions though, friends can call each other attractive too, mostly between girls. For example, some girls are getting dressed up for a fancy dinner, girl A says to B, "Wow Sarah, you look really attractive in that dress!", and this would just be seen as a compliment.