Suppose that a random variable $X$ has a gamma distribution with the shape parameter, $\alpha$, and the scale parameter, $\beta$, i.e., $X \sim \mathrm{Ga}(\alpha, \beta)$. It is well known that $\mathrm{Ga}(1, \beta)$ is the same as an exponential distribution, $\mathrm{Ex}(\beta)$.
Which is appropriate, $\mathrm{Ga}(1, \beta) = \mathrm{Ex}(\beta)$ or $\mathrm{Ga}(1, \beta) \stackrel{d}{=} \mathrm{Ex}(\beta)$ ?