cleanIAT function in R IAT package
So I'm the author of the IAT package in R. It's based on the original scoring algorithm outlined in this publication. Because the scoring algorithm is based on a standard 7-block IAT, the score IAT1 corresponds to the D score relative to the difference between blocks 6 and 3, while IAT2 corresponds to the D score relative to blocks 7 and 4. IAT is then simply the mean of IAT1 and IAT2, and represents the overall D-score of the test. In a simple applied example, you might use this variable as the outcome in a simple t-test to see if there is an effect of some treatment group versus a control group.

One thing to keep in mind when using the IATData loaded with the package is that there are order effects due to randomization of whether participants received stereotype congruent sorting first or stereotype incongruent sorting first. Thus, the D score needs to be calculated separately between these two groups, otherwise the D score would be flipped for half of the participants (see the example in ?cleanIAT to see what I mean).

As for discrepancies, I never tested against SPSS code, but it was designed to replicate the SAS macro used by the Nosek lab exactly.

Finally, a faster version using dplyr is available for download off of my github if you're interested:

library(devtools)
install_github("dpmartin42/IAT")