That is a good distinction. I suppose the question from Reformed Baptists would be how do we know to have that trust since we can never be certain of anyone else's faith but our own? We would say that the Bible gives us many examples of "reasonable expectations" based on a profession of faith.
That is because Calvinist infant baptizers don't want to presume that God has not decreed that this infant is reprobate [i.e. divinely decreed not to receive saving grace, and divinely decreed to be tormented in hell fire eternally]. When they say, "I trust God that my child is a member of His family", that really means only, "I hope that my child is a member of His family." If Calvinists believed that God had promised that through baptism the infant is made a member of God's family, they could say after the child's baptism "I know that my child is now a member of God's family", since if God promises X, one can know X, not just hope that X. But they explicitly refuse to say "I know that my infant is now a member of God's family" because they have no reason to believe that the likelihood of the infant's reprobation is less than the likelihood of the infant's election. When their baptized infants die, they do not know whether the infants go to heaven or hell. They just hope, as one might hope waiting for the lottery numbers to be anounced, that their infant was among the elect and not the reprobate.
-A8
But our "profession of faith" isn't the combination to some lock that we've now been given. We profess our faith because God tells us to do so, and we're able to do this when He gives us the understanding that Christ died on our behalf. But our membership in the covenant family doesn't depend on our acknowledgment, but on God's adoption.
I know I linked you to one of Dr. MaMahon's articles from his website, A Puritan's Mind. He was raised and ordained a Baptist and then became a Presbyterian pastor. I think his explanation of his journey is really very good. Here are a few of his essays...
I'm going to spend some time reading these by McMahon and also this oldie but goodie by B.B. Warfield...
And then there's always Calvin for brevity and specificity...
"The offspring of believers are born holy, because their children while yet in the womb, before they breathe the vital air, have been adopted into the covenant of eternal life. Nor are they brought into the church by baptism on any other ground than because they belonged to the body of the Church before they were born. He who admits aliens to baptism profanes it. . . . For how can it be lawful to confer the badge of Christ on aliens from Christ. Baptism must, therefore, be preceded by the gift of adoption, which is not the cause of half salvation merely, but gives salvation entire; and this salvation is afterwards ratified by Baptism.""Let Joachim say, in one word, what weight he attaches to the promise, - I will be thy God, and the God of thy seed. If God did not ingraft into the body of his people those on whom he bestows this high privilege, not only is injury done to his word, but infants ought to be denied the external sign. Let an Anabaptist come forward and maintain that the symbol of regeneration is improperly conferred on the cursed children of Adam whom the Lord has not yet called to the fellowship of his grace. Either Westphal must remain dumb, or the only defense that can avail him is, that the grace which was offered in the person of their parents is common to them. Hence it follows, that they are not absolutely regenerated by baptism, from which they ought to be debarred, did not God rank them among the members of his Son."