The first Cronbach's alpha employs the covariances among the items, whereas the alpha based on standardized items employs the correlations among items. The latter alpha is based on the assumption that all of the items have equal variances, which is often false in practice. The alpha that is reported in the "Cronbach's Alpha If Item Deleted" column is the first Cronbach's alpha, i.e., the alpha that is NOT based on standardized items.
The formulae for Reliability statistics can be found in the case studies for Reliability that are available in the "Help>Case Studies" menu of SPSS. Expand the Table of Contents section for Statistics Base, then scroll down to the link for "Measures of Reliability in Scale Problems". More complete coverage of formulas for RELIABILITY is given in Help>Algorithms>RELIABILITY Algorithms