No change in position vector, yet a non-zero magnitude for change in magnitude for the vector?

In the book "Fundamental Laws of Mechanics" by I.E Irodov, on page 15, he writes as a footnote,

note the in general case $ |mathrm{d}textbf{r}| neq mathrm{d}r$ where $r$ is the modulus of the radius vector $textbf{r}$, and $ v neq frac{mathrm{d}r}{mathrm{d}t}$. For example, when $textbf{r}$ changes only in direction, that is the point moves in a circle, then $ r= textit{const}$; $mathrm{d}r=0$ but $ |mathrm{d} textbf{r}| neq 0$.

The reason this doesn’t make sense to me, is suppose we have a position vector modelling circular motion, suppose,

$$vec{ r(t)} = vec{r_o} + ( cos theta vec{i} + sin theta vec{j})$$

Where, $ theta$ is a function of time (with $ frac{d theta}{dt} =omega$ and $r_o$ is a constant vector, then,

$ mathrm{d(vec{r})} = omega ( -sin theta vec{i} + cos theta vec{j}) dt $

now,

$ |mathrm{d(vec{r})}| = omega dt$

Now, neither of these are zero, so I’m looking for a simpler explanation of what Irodov is saying