Can we differentiate between observed sequences of IID and uncorrelated noise?
It is not clear what exactly the OP understands or means by the various words in the phrase

either a White-Noise process or an IID process, i.e. both are uncorrelated however the former also is independent,

For example, the initialism IID usually stands for &quot;independent identically distributed&quot;, and so &quot;IID process&quot; usually means a sequence of independent identically distributed random variables. If readers agree that this is the accepted meaning, then the OP's statement that the random variables constituting the process are uncorrelated is perfectly true, but the very next words &quot;former also (emphasis added) is independent&quot; suggests that the OP thinks that the random variables constituting the IID process are not independent, uncorrelated though they happen to be. Of course, those who don't accept the generally accepted meaning of IID will have their own version of what is the truth and what is a BIG LIE.
Similarly, it is not clear what the OP understands by &quot;White-Noise process&quot;, except that the random variables constituting the process are independent random variables (and hence uncorrelated random variables). Are there any other requirements that might be reasonable to impose on the random variables constituting the White-Noise process? Zero mean, maybe? Symmetric distribution about $0$? Identical Distribution? or is something like $X[n] \sim \mathcal N(0,1)$ for even $n$ and $X[n] \sim \mathcal N(0,2)$  for odd $n$ acceptable? And if so, what is the justification for this belief about the properties of a White Noise process?
There is a long-standing tradition on dsp.SE to say that (discrete-time) white noise is nothing more than a sequence of uncorrelated random variables and that independence is not required, and should not be insisted upon. I disagree with this school of thought because (i) correlation is a pairwise relation whereas independence is a more general property involving more than two random variables and (ii) lack of correlation only tells us that linear estimation/prediction is not useful but says nothing about more general nonlinear estimators/predictors.  A canonical example is of $X 
\sim \mathcal N(0,1)$ and $Y = X^2$ which are uncorrelated random variables and yet $Y$ is a (nonlinear) function of $X$. As another example. consider the following from @MarcusMuller's answer to this question:

Dependent, but uncorrelated (in the pair-wise sense)
Also, $Y_i$ be a discrete time process. Define:
$$Y_i \begin{cases}
&gt;\sim U\{-1,+1\} &amp;\text{randomly, independently}&amp;  \text{ for }i \ne 3N,\\
&gt;=Y_{i-1}\cdot Y_{i-2} &amp;\text{(fixed!)} &amp; \text{ for }i=3N
&gt;\end{cases}.$$

Indeed, $Y_1, Y_2,$ and $Y_3 = Y_1Y_2$ uncorrelated random variables, but in fact, $Y_1, Y_2, Y_3$ are pairwise independent random variables too.  However, $Y_1, Y_2, Y_3$ are not mutually independent random variables.