Difference in specifying equations

I wanted to ask if the following two are similar. I ran IRFs and both of them gave me the same plots. However, it differs in the “policy and transition functions”.

The first one:

pi = RHO*pi(-1)+ e;
var e; stderr=0.25;

The second one:

sig_e = 0.25;
pi = RHO*pi(-1)+sig_e * e;
var e; stderr=1;

That is expected, because you rescale the impact of the shock e. But the specifications are isomorphic.

Great, thanks for your reply.