Is there a difference between "co-redeemer" and "co-redemptrix"? Did Pope Francis throw cold water on any hope for a 5th Marian dogma or is there a fundamental difference between &quot;co-redeemer&quot; and &quot;co-redemptrix&quot; that leaves the door slightly ajar?
Is there a difference between “co-redeemer” and “co-redemptrix”?
Technically co-redeemer is masculine and co-redeemptrix is female.

Definition of co-redemptrix
A woman whose participation is believed by some Roman Catholics to be essential for the redemption of humanity
Specifically: Virgin Mary

The title of co-redeemer is occasionally applied the the Virgin Mary:

Mary's title of Co-Redemptrix or Co-Redeemer can assist in magnifying our understanding of God's humility. - Teachings Not Yet Declared Dogmas
Co-Redemptrix or Co-Redeemer

Yes, it seems Pope Francis did throw cold water on any hope for a 5th Marian dogma!

At his weekly public audience on March 24, 2021, Pope Francis rejected the claim that the Virgin Mary should be honored as “co-redemptrix,” saying that she should be honored, “but as a mother, not as a goddess, not as co-redeemer.” Noting that he was speaking on the eve of the Annunciation feast day, he pointed out that in Christian iconography, the depiction of Mary is “always in relation to her Son and in connection with Him.. she always points out the center: Jesus.” - Catholic News Headlines

Although Pope Francis was not speaking ex cathedra, he definitively makes a point that he does not favour such a dogma.

Christ is the Mediator, Christ is the bridge that we cross to turn to the Father (see Catechism of the Catholic Church, 2674). He is the only Redeemer: there are no co-redeemers with Christ. He is the only one. He is the Mediator par excellence. He is the Mediator. Each prayer we raise to God is through Christ, with Christ and in Christ and it is fulfilled thanks to his intercession. The Holy Spirit extends Christ’s mediation through every time and every place: there is no other name by which we can be saved: Jesus Christ, the only Mediator between God and humanity (see Acts 4:12).
Due to Christ’s one mediation, other references Christians find for their prayer and devotion take on meaning, first among them being the Virgin Mary, the Mother of Jesus.
She occupies a privileged place in the lives of Christians, and therefore, in their prayer as well, because she is the Mother of Jesus. The Eastern Churches have often depicted her as the Odigitria, the one who “shows the way”; and the way is her Son, Jesus Christ. The beautiful, ancient painting of the Odigitria in the Cathedral of Bari comes to my mind. It is simple. The Madonna who shows Jesus, naked; then they put a shirt on him to cover his nakedness, but the truth is that Jesus is naked, he himself, man, born of Mary, is the Mediator. And she indicates the Mediator: she is the Odigitria. Her presence is everywhere in Christian iconography, sometimes very prominently, but always in relation to her Son and in connection with Him. Her hands, her eyes, her behavior are a living “catechism”, always indicating the hinge, she always points out the center: Jesus. Mary is completely directed toward Him (see CCC, 2674) to such an extent that we can say she is more disciple than Mother. The directions she gave at the wedding at Cana: “He: do whatever he will tell you”. She always refers to Christ. She is the first disciple.
This is the role Mary fulfilled throughout her entire earthly life and which she forever retains: to be the humble handmaid of the Lord, nothing more. At a certain point in the Gospels she almost seems to disappear; but then she reappears in the more crucial moments, such as at Cana, when her Son, thanks to her caring intervention, performs his first “sign” (see Jn 2:1-12), and then on Golgotha at the foot of the cross. - General Audience, 24.03.2021

Wikipedia has the following to say about the title of co-redemptrix:

According to those who use the term, Co-Redemptrix refers to a subordinate but essential participation by the Blessed Virgin Mary in redemption, notably that she gave free consent to give life to the Redeemer, which meant sharing his life, suffering, and death, which were redemptive for the world. Related to this belief is the concept of Mary as Mediatrix, which is a separate concept but regularly included by Catholics who use the title Co-Redemptrix. A Fifth Marian Dogma has been proposed including both Mediatrix and Co-Redemptrix.
The term Co-Redemptress was used by Pope Leo XIII in 1894. &quot;For in the Rosary all the part that Mary took as our co-Redemptress comes to us...&quot;
The concept was especially common in the late Middle Ages, when it was promoted heavily among the Franciscans, and often resisted by the Dominicans. By the early 16th century the hopes of the concept becoming Catholic doctrine had receded, and have never seriously revived. In more recent times, the title has received some support from the Catholic Magisterium though it is not included in the concluding chapter of the apostolic constitution Lumen gentium of the Second Vatican Council, which chapter many theologians hold to be a comprehensive summary of Roman Catholic Mariology. Some, in particular the adherents of the Amsterdam visions, have petitioned for a dogmatic definition, along with Mediatrix, and the process for further theological clarification and eventual dogmatic definition is ongoing. Pope John Paul II was the most favorable of recent Popes. As a Cardinal, Pope Benedict XVI suggested that the Marian title caused confusion and did not sufficiently reflect scripture. Pope Francis has repeatedly suggested the title not be used. - Co-Redemptrix