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Correlation coefficient (Pearson’s r)
A number between $-1$ and $1$ that measures the strength and direction of a linear relationship between two variables.
Pearson’s product-moment correlation coefficient (PMCC)
A standardized measure of linear correlation given by
$$r=\frac{\frac{1}{n}\sum xy-\bar{x}\bar{y}}{\sigma_x\sigma_y},$$
where $\sigma_x$ and $\sigma_y$ are the standard deviations of $x$ and $y$.
Standard deviation
The (population) standard deviation is the square root of the variance, that is, the square root of the mean of the squared deviations from the mean. For a population,
$$
\sigma=\sqrt{\frac{\sum(x-\mu)^2}{n}}
$$