The types of correlations available in the Correlation matrix box on the Reliability and Item Analysis (Startup Panel) - Advanced tab are described here.

Standard Pearson r. Select Standard Pearson r to compute the standard Pearson product-moment correlation coefficients. The reliability analysis will be based on those correlations.

NO. Select NO to suppress the calculation of the correlation matrix in order to speed up calculations. Note that if more than 100 variables (items) are selected, the correlation matrix will not be computed and this option will automatically default to NO. However, you can compute an overall correlation matrix for more variables (e.g., 500 or more, depending on the amount of memory available in your computer) via the Correlation matrices option from the Basic Statistics and Tables (Startup Panel) - Quick tab

Tetrachoric r (quick cos p approx.). Select Tetrachoric r (quick cos p approx.) for the analysis to be based on tetrachoric correlations, computed via the cosine pi formula (applicable to dichotomous data) that yields up to 4 digits of precision, as long as the proportions (i.e., the number of 0's and 1's) are not extreme (e.g., 95% 0's and 5% 1's).

Tetrachoric r (iterative approx.). Select Tetrachoric r (iterative approx.) for the analysis to be based on tetrachoric correlations, computed using a more time-consuming but also more precise procedure based on Gaussian quadrature and Newton-Raphson iterations (see Kirk, 1973). This iterative procedure is considerably slower than the above tetrachoric correlation procedure.

Tetrachoric correlations are not recommended for most standard analyses (consult the Introductory Overview for details).