"False friends", "trap words", or, technically, "deceptive cognates"
"Cognates" are words in different languages that share a common origin and show some degrees of similarity. "Cognate" is itself one of these words: It. "cognate" are Eng. "sisters-in-law".
In the case of Eng. and It., the common origin is usually Latin. Most cognates are helpful: the examples presidente, congresso, stazione, virtý, fantasia... for "president, congress, station, virtue, fantasy"... were mentioned in the home page, and a lot more can be added to the list. But here we focus on differences.
It is important to bear in mind that words that can be deceptive can belong to different groups. "Morbido", also mentioned in the home page, never means "morbid". "Un letto morbido" is a soft bed. Incidentally, there is another It. word that translates "morbid" and is "morboso".
Other words, instead, may be true friends in some cases and false friends in other cases. One example is Eng. "bust", similar to It. "busto, busta". The latter means "envelope", so it is a totally false friend. "Busto", instead, has several meanings and one of them, "a type of statue with only head and shoulders", corresponds to one of the several meanings of "bust": so it is a partially true friend. An enormous lot of words, in fact, have several meanings.
Finally, there are words whose spellings are quite similar or even coincide in the two languages but are not cognates. It. "sale", for example, is three different words, that can be differentiated by means of grammatical devices: "il sale, le sale, lui sale" or by means of lexical devices: "sale e pepe, sale e salotti, sale e scende." The three words, in Eng., are "salt, halls, goes up" and none of them is related with Eng. "sale", the act of selling.