With this type of clue the setter inserts a word to hint that there is a word hidden within. In this clue some tells us that the answer is some of the clue. In this case chicken. Other words that might indicate a Hidden Word Clue include in, from, inside, partly, and so on. These are all words that hint at something hidden.
Homophones are clues where the solution sounds like one thing but is spelt differently.
When the clue is a Homophone the setter inserts a phrase or word that suggests that we think about the sound of the word. Since a mouthful is a bite the answer is probably byte. Other words that might indicate a Hidden Word Clue include say, we hear, verbally, mouthed, to the audience, and so on. These are all words that hint at sound. Here are some other examples of Hiddens and Homophones.