Dear Javier,

The difference is in the priesthood.

In the first place, the consecrated person who is not a priest obviously cannot do priestly ministry (principally the celebration of the Eucharist and hearing Confession). But even when doing the things that others can do (preaching, teaching, ordinary administration, etc.) the priest is different. This is because of the priestly character on his soul. His actions are united to Christs in a special way due to his priesthood, and have a special value in that priesthood. You can also say that since he is a priest, for many of the faithful with whom he will work, even though it is in ordinary, non-sacramental things, his example and action will have a special impact and force.

God bless.  Fr Anthony