Change reference group in logistic regression analysis

Hello,

I have a data set including a binary outcome variable "med" coded as 0 and 1. Predictors include "score" (low=0, medium=1, high=2) and "age".

I use Stata 14.1 and run the following command:
logit med i.score age, nolog
then I got this model:
logit(med)=cons+a*age-0.74*score1-0.86*score2
(Both P for -0.74 and -0.86 are less than 0.05)

Now I want to change the reference group to high (2). I use the following command:
logit med ib2.score age, nolog
then I got this model:
logit(med)=cons2+a*age+0.86*score0+0.12*score1
(P for 0.86 is less than 0.05 but P for 0.12 is over 0.05)

So I am wondering if the reference group is changed, the model will become a totally different model? Is this correct? (As I think the model should be the same no matter whether I change the reference group or not.)

Thank you!