I am confused about the effect of multiplier and offset in declaring data in Stan. Actually after reading the reference manual I am confused about the following example:

As an example, we can give `x`

a normal distribution with non-centered parameterization as follows.

```
parameters {
real<offset=mu,multiplier=sigma> x;
}
model {
x ~ normal(mu, sigma);
}
```

Recall that the centered parameterization is achieved with the code

```
parameters {
real x;
}
model {
x ~ normal(mu, sigma);
}
```

What’s the difference between the ‘non-centered parameterization’ and ‘centered parameterization’ here? Are these two Stan code refering to the same model?