Cross correlation, when two signals are "uncorrelated"? Definition of cross correlation is

$$
\int_{\mathbb{R}}s_1^*(\tau)s_2(t+\tau)d\tau
$$

I wonder using such definition, when two signals are not correlated? My guess is the following...
defining
$$
s_{2,\tau}(t) = s_2(t+\tau) = \left(T_{-\tau}s_2\right)(t)
$$

We have

$$
\langle s_1,T_{-\tau}s_2 \rangle = 0
$$

for all $\tau$, namely $s_1$ is orthogonal to all the signals $s_{2,\tau}$. Is this guess correct?

This definition is taken from Wikipedia.

As assumption you can assume $s_1,s_2 \in \mathcal{L}^2(\mathbb{R})$, the definition should be then well posed by the Cauchy-Schwarz inequality.
Cross correlation is a measure of similarity between two signals, where one signal is allowed to be time-shifted. In this sense, the correlation is not a single number, but a function of the time shift. We say, "these two signal have a certain correlation $R(\Delta)$ for a time shift $\Delta$".

Intuitively, two signals that tend to have the same sign (both positive or both negative) for a given time shift $t$ are similar, and will have large correlation (positive or negative). Signals that are uncorrelated are just as likely to have opposing signs, and then the integral will be small.

As an example, consider two signals that are rectangular pulses of duration $T=1$, but one starting at $t=0$ and the other at $t=10$. Their product is zero (and thus their correlation for time shift 0 is also 0). However, intuitively we could say that they are similar, except for the delay. Thus, the correlation allows us to quantify that intuition: these two pulses are completely uncorrelated for some delays; however, when if the first is time-delayed by 10 seconds, then they become highly correlated.

Note that $R(\Delta)=0$ is a sufficient and necessary condition for the two signals to be "uncorrelated" (meaning they have zero correlation) with time shift $\Delta$.