Is there only one internal semidirect group?

Question

I am a bit confused on the concept of internal semidirect group $N\rtimes H$.

For external semidirect group $N\rtimes_\varphi H$, I know that there can be possibly many semidirect groups depending on the homomorphism $\varphi: H\to\text{Aut}(N)$.

For internal semidirect group $N\rtimes H$, is there only one such group, where the homomorphism is taken to be conjugation, i.e., $\varphi_h(n)=hnh^{-1}$?

Thanks for the clarification.