What are the differences among different notions of harmonic maps?

Question

Given smooth (compact, if needed) Riemannian manifolds $M$ and $N$. There are at least 3 different notions of harmonic maps (shortly, HM):

1. weakly HM.

2. stationary HM.

3. minimizing HM.

It is well-known that a smooth weakly HM must be stationary.

Question 1: What are the difference among the 3 notions of harmonic maps?

Question 2: Given a weakly HM $u:M \rightarrow N$, if it is smooth, is it true that $u$ must be a (locally) minimizing HM? Why?