Interpreting this plot cross-correlation
Autocorrelation of $x$: at zero shift, the two signals being correlated ($x(t)$ and $x(t)$) are identical, hence a large correlation. At any other shift ($x(t)$ and $x(t+\tau)$), the correlation is near zero (no correlation). Some noise there is expected.

Autocorrelation of $y$: at zero shift, as always, there is maximum correlation of the two signals. Because the signal is smooth, correlation changes slowly with increasing shift. At various shifts peaks line up an the correlation has a local maximum.

Crosscorrelation of $x$ and $y$: you’re not showing the magnitude of the y-axis, I presume it’s small because the signals are not correlated. At some shift (it just happens to be close to zero, this is coincidence) there is the absolute maximum because it has to exist somewhere. Again, because $y$ is smooth, the correlation changes smoothly with the shift. But in general you’re looking at smoothed noise here.

If you computed the crosscorrelation by padding the input with zeros (rather than using the circular periodicity imposed by the Fourier transform) then you would expect the peak to be close to 0, as the correlation for larger shifts will include more of the zero values in the padding (the signals overlap less, hence the sum of their point-wise multiplication is closer to 0).