I've learned sum of exponential random variables follows Gamma distribution.

But everywhere I read the parametrization is different.  For instance, Wiki describes the relationship, but don't say what their parameters actually mean?  Shape, scale, rate, 1/rate?

Expoenetial distribution:  $x$~$exp(\lambda)$
$$f(x|\lambda )=\lambda {{e}^{-\lambda x}}$$
$$E[x]=1/ \lambda$$
$$var(x)=1/\lambda$$

Gamma distribution: $\Gamma(\text{shape}=\alpha, \text{scale}=\beta)$
$$f(x|\alpha ,\beta )=\frac{1}{{{\beta }^{\alpha }}}\frac{1}{\Gamma (\alpha )}{{x}^{\alpha -1}}{{e}^{-\frac{x}{\beta }}}$$
$$E[x]=\alpha\beta$$
$$var[x]=\alpha{\beta}^{2}$$

In this setting, what is $\sum\limits_{i=1}^{n}{{{x}_{i}}}$?  What would the correct parametrization be?  How about extending this to chi-square?

Thanks!