From definition 1 of Meinshausen(2007), there are two parameters controlling the solution of the relaxed Lasso.
The first one, $\lambda$, controls the variable selection, whereas the second, $\phi$, controls the shrinkage level, when $\phi= 1$ both Lasso and relaxed-Lasso are the same, and for $\phi<1$ you obtain a solution with variable closer to what would give an orthogonal projection on the selected variables (kind of soft debiasing).

This formulation actually corresponds to solve two problems:

1. First the full Lasso with penalization parameter $\lambda$
2. Second the Lasso on $X_S$, which is $X$ reduced to variables selected by 1, with a penalization parameter $\lambda\phi$.

Hope this will help.

From definition 1 of Meinshausen(2007), there are two parameters controlling the solution of the relaxed Lasso.

The first one, $\lambda$, controls the variable selection, whereas the second, $\phi$, controls the shrinkage level. When $\phi= 1$ both Lasso and relaxed-Lasso are the same (as you said!), but for $\phi<1$ you obtain a solution with coefficients closer to what would give an orthogonal projection on the selected variables (kind of soft de-biasing).

This formulation actually corresponds to solve two problems:

1. First the full Lasso with penalization parameter $\lambda$
2. Second the Lasso on $X_S$, which is $X$ reduced to variables selected by 1, with a penalization parameter $\lambda\phi$.