generating white gaussian noise in matlab using two different functions
A white noise sequence is one for which each (random) element is uncorrelated from every other element:
$$
E[y[n]y[m]] = \left \{ \begin{array}{ll}
0 &amp; \mbox{for } n\not=m\\
\sigma_y^2 &amp; \mbox{for } n = m
\end{array}
\right . \\= \sigma_y^2 \delta[n-m]
$$
where $\sigma^2_y$ is the variance of $y$.

Note that I am assuming (because of the whiteness) that the signal is zero mean.

The whiteness of a signal says nothing about the distribution of its values.  To know something about that, Gaussianity or some other distribution needs to be invoked.

The functions wgn and randn both produce white, Gaussian noise sequences.

Calling the function rand would produce a white, uniformly distributed noise sequence.