Alter Christus is what every Christian should be in their daily life. This is particularly true for the priests. It means "another Christ." The priest is a representative of Christ to the Christian community.
"In persona Christi" is how the priest acts in his administration of the sacraments. The priest as an "Alter Christl" does not act on his own during the administration of the sacraments. He acts in persona Christi, that is Christ acts through the priest in the administration of the sacraments. For example, when you go to confession and recieve absolution you don't recieve absolution in the name of the priest himself, you recieve it from Christ who acts through the priest. The priest acts "in persona Christi" and not on his own.
I hope this is helpful.
I had someone once say that we can never contradict a priest because their an "alter Christus".
She meant it in such a way to almost kiss the ground the priest walked on, to the point of overlooking many possible faults.
And we ought to overlook his behavior because he is an "alter Christus".
Is there catholic teaching that backs this up?
I teach my children that everyone (especially priests) deserve a certain level of respect.
But the priest is also human, ergo fallen nature - just like each and everyone of us, and will err.
So even if he is an "alter Christus", we cannot expect him to always behave like Christ.
I encourage my children to always pray for our priests, to keep them out of trouble, and to take them out of it if they already are.