To start, let's define our terms. There are three kinds of close-ups: medium close-up, close-up (close shot), and extreme close-up. When film directions say simply "close-up," the close shot is meant.
Medium close-ups show shoulders to head and may have background or other characters in the shot as well. The close-up is a head shot or a close shot of some other element, like hands, a painting, a shoe, etc; background and other characters are almost exclusively excluded from the close-up. An extreme close-up shows one feature of the character, usually eyes or lips, but may, like the medium close-up, focus on some other element, like fingers, a book, etc.
There are a good many medium close-ups in this film. Whenever Cinderella converses with anyone, both characters are often in medium close-up (shoulders to head). There are many medium close-ups of hands, as well, which is a thematic element. Da Vinci's two art works (Mona Lisa and Cinderella) are also shown in medium close-up.
Close shots are fewer. The Prince is shown in close-up (head only, little or no background) when he talks in the palace gardens with his mother, the Queen, about the false report of Cinderella's betrothal. The Queen is also shown in close-up after him. Later, when the Prince is dressed for the ball, he is shown in close-up, melancholy in the corridor. After the King approaches him, the King is also shown in close-up.
For clarity's sake, point-of-view shots are sometimes confused with reaction shots, which are cuts from one character to another, or from a scene to a character. These show character's reactions to each other or to the preceding event or action and are often used to film conversations. Contrastingly, a point-of-view shot is one that takes the place of the character and stands where the character is standing and moves as the character is moving.
A point-of-view shot (POV shot) occurs when the Prince leads Cinderella through his secret garden, then again when Cinderella looks at the view of the uppermost garden branches. In both instances, the camera stands in for the character's movement and vision. A brief POV shot occurs when the wicked stepmother and her two daughters (one wicked, one good) walk up the Reception Room approaching the King and Queen's thrones. For a brief shot, the camera walks up in the place of the characters and shows the King and Queen gradually coming closer to the characters.