They are the same thing in the sense that they both model Abbott's correction, probit[ (y-c)/(1-c) ], as a linear function of the predictors, where c is the natural threshold rate. See the Overview section of the PROBIT documentation. Details on the method are in the Finney reference in the PROBIT documentation. I am not sure if what you consider Abbott's formula estimates c in a particular way, but PROBIT estimates is along with the model parameters by maximum likelihood estimation. If what you are looking at estimates in some other way, then that would explain the difference you see. Note that if you estimate c by some other means, or have a prior estimate, you can specify it in PROBIT using the C= option. In that case, omit the OPTC option to avoid modifying the specified value.
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