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The difference between a disc (disk) and a circle is crystal clear to me:

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However, in many children's books, a disc is usually called a circle:

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Why do many children's book confuse discs with circles? Should we teach children the difference between a disc and a circle?

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    $\begingroup$ The underlying reason could probably be the dual meaning of circle in everyday English. Thus, confusion wouldn't be the best word to describe the situation. $\endgroup$
    – Michał Miśkiewicz
    Commented Mar 25, 2022 at 15:41
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    $\begingroup$ I see an annulus and a disk. $\endgroup$
    – Thierry
    Commented Mar 25, 2022 at 18:00
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    $\begingroup$ This isn't "confusion", this is (appropriately) using one of the the ordinary English meanings of the word "circle" rather than the technical mathematical definition. $\endgroup$
    – Henry Towsner
    Commented Mar 25, 2022 at 21:36
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    $\begingroup$ Are you perhaps implying that the surface area of a circle is zero? $\endgroup$
    – knl
    Commented Mar 25, 2022 at 23:18
  • $\begingroup$ @JoelReyesNoche, you are right. The formula $\pi r^2$ gives the area of a disc, while the area of every circle is zero. $\endgroup$
    – Zuriel
    Commented Mar 27, 2022 at 1:46

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Mathematics, as any other field of inquiry, has specific terminology. The rest of the world is not obliged to use the same technical terminology.

Note that this also happens within mathematics; not every subfield is interested in the same issues and sees the same distinctions as important.

In particular, for young children, the relevant thing to learn is the names of basic figures, together with names of colours, and so on. The minute difference between a circle and a disk is not relevant for a number of years. (Why minute: you have a one-to-one correspondence, so identifying them with each other is quite reasonable for many purposes, even for a professional mathematician. It is usually clear which one we are talking about.)

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