R and Stata show different results when I run zero-inflated Poisson in each program. Why does this occur? I ran zero-inflated Poisson in both R and Stata using the same dataset and the same variables and found out the coefficients of the results are different. I found out that Poisson is set as a default distribution and logit is set as a default link in both programs. I am not sure if R and Stata use different optimization methods and this yields results that are different from each other.
Also, I used zeroinfl function in pscl package for R, and used zip function for STATA.
In other words, my code looks like
zeroinfl(y ~ x1 + x2 | x1 + x2, data = data) in R,
zip y x1 x2, inflate(x1 x2) in Stata

Stata and the pscl package may well use different optimization algorithms, so you could expect coefficients to differ slightly between models fitted on different software.
I fitted zero-inflated models to the sample dataset (bioChemists) included with the pscl package. I can't easily import the output here, as I have Stata on a remote server. I can attest that for this data, the coefficients are identical to within 4 or so decimal places, provided I use the same base level for categorical covariates (the sign flips if not).
By my reading, the commands as you typed them for both packages should use the same covariates in both parts of the model. In some cases, packages may use different parameterizarions. For example, SAS and Stata parameterize the cut points in ordinal logit models a bit differently, so the interpretation of the cut points is different. That should not be the case with these two softwares.
