In a 1957 encyclical titled Invicti Athletae, Pope Pius XII wrote:
... non solum profuso sanguine fidei nostrae testimonium Deo praebetur ...
which the official translation renders
... not only by shedding of blood is the witness of our faith given to God ...
This refers to shedding of one's own blood: the "unconquered athlete" in question is the martyr St. Andrew Bobola.
On the other hand, Pope St. John Paul II's 1995 encyclical Redemptoris Missio contains the passage
... est etiam inscripta in historia humani generis sanguine effuso ob ideologias et a rebus publicis ...
which again translators render
... it is also written in the history of humanity with the blood shed in the name of ideologies ...
where here the "blood shed" is clearly that of another.
Granted that it's not clear that either of these were originally written in Latin, is the distinction between profusus and effusus simply an authorial or editorial preference, or does ecclesiastical Latin routinely make a distinction of this sort?