Tetrachoric correlation is used to measure rater agreement for binary data; Binary data is data with two possible answers—usually right or wrong. The tetrachoric correlation estimates what the correlation would be if measured on a continuous scale
Polychoric correlation measures agreement between multiple raters for ordinal variables (sometimes called “ordered-category” data). Ordinal variables can be placed in order, but can’t be divided or multiplied.
The point-biserial correlation coefficient is a special case of Pearson’s correlation coefficient. It measures the relationship between two variables when one continuous variable (must be ratio scale or interval scale) and one is a naturally binary variable.
Biserial correlation is almost the same as point biserial correlation, but one of the variables is dichotomous ordinal data and has an underlying continuity.
Polyserial correlation is between a quantitative variable and an ordinal variables, based on the assumption that the joint distribution of the quantitative variable and a latent continuous variable underlying the ordinal variable is bivariate normal.