It can mean both. I was just unsure of how common a word puree is in English.
Just remember that it is the skill to practice reading the Cyrillic alphabet used in Russian. Some words are chosen just for the letters they have (пюре has a Ю, for example). Медик (medic), пюре (purée), велосипед (bike), багаж (luggage), рюкзак (backpack) are by no means rare: these words are known by any native speaker. However, these are not extremely common words either; they are somewhere in the middle. If no alphabet exercises were necessary, we would have some other words at the beginning.
I didn't know. :D In English puree is a very commonly known word, just not for potatoes, hence the confusion some people have with this. I also speak Spanish and Portuguese, in which mashed potatoes is simply called "puré".
I understand the reasoning behind using puree as a means of teaching the alphabet, and it's a good thing to know. :)
My Russian professor explained that the weird pronunciations of some Russian words is because they are usually the most commonly used. Over time the pronunciation shifts to where they "eat" certain letters because they have to say it all the time. So пожалуйста turns into something sounding to us like "pahzhalsta".
In English a good example is Christmas. Instead of Christ mass it's "crissmas"
Пюре is usually enough. There are two primary purees we might mean—mashed potatoes and fruit puree sold in small cans. I think the former is a more common meal by a large margin (unless you are a baby), so it makes no harm to omit картофельное in most real-life scenarios.
In a similar fashion, if you are talking about baby food you may just say пюре (as long as the listener knows the context).
"Пюре, пожалуйста." Is written as a complete sentance, which I gather it is in Russian. Is Russian looser than English in this respect? The translation is given as "Mashed potatoes please." as though it were a complete sentance; a proper English sentance requires a verb, so this is a mear phrase, with no initial capital or punctuation needed.