Different results between Parameter estimates and Indicator function parameterization

[#1]

Dear,

I performed a regression model consisting of 9 terms (main effects and interactions). The 4 variables used in this model are categorical variables which all have 2 levels. Since, I am a SAS user I prefer the Indicator function parameterization over the parameterization of JMP. However, I noticed some discrepancy between the p-values of the parameter estimates table and the Indicator function parameterization. For 1 interaction in the model, the parameter estimates table provide a p-value of 0.0046 and the Indicator Function Parameterization gives a p-value of 0.5173. This is the only term that changes from being significant to non-significant when changing the parameterization. Not sure if this is helpful information, but the standar errors in the parameter esitmates table are the same for all model terms. Could someone please explain me what could be the reason behind this? 

Thanks in advance.

[#2]

The Parameter Estimates table includes p-values for the null hypothesis that the parameter equals zero. The parameterization determines the estimates and the meaning of the parameter for categorical predictors. They are not supposed to be the same.

[#3]

Thanks @Mark_Bailey for your response.

I'm aware that using a different parameterization will end up in different p-values. However, I did not expect that based on the paremeterization a p-value for a given term will go from significant to non-significant. That's quite a big difference. Is there something behind the parameterization JMP uses that results in a significant term while the GLM parameterization ends up in a non-significant value for the same term?

[#4]

The documentation explains both the coding for each parameterization and the interpretation of the parameters under each scheme. The terms represent different effects under each parameterization, so, of course, there is no reason that a term should necessarily be significant under both parameterizations.