I have found it quite confusing to try and understand what traditional Reformed circles mean precisely in their doctrine of "limited/definite atonement", particularly as not all theologians describe it in quite the same way, and the Fallacy of Equivocation seems sometimes to play quite an important role in Reformed theological philosophical reasoning.
Is it the case that a substantial proportion of those theologians and church leaders today who consider themselves of a traditional Reformed persuasion would be willing to affirm the following 4 points?
The underlying motivation [as described e.g. in John 3:16] behind God's plan of atonement through Christ did not involve love for humanity as a whole, either in a corporate sense as the race of descendents of Adam, or individually towards all the sinners that would ever live. Rather, the love underlying God's plan of atonement concerned only His elect people throughout the world (both corporately and individually).
Christ's suffering under the wrath of the Father was sufficiently great to be able to pay for all the sin ever committed. Nonetheless, the wrath itself that Christ faced on the cross did not involve wrath corporately against the sin of the human race as a whole, nor did it include all of God's wrath against every sin ever committed by a human. It consisted exclusively of God's wrath against all sin that was against the account of elect people.
Christ's atoning sacrifice did not create any means of mercy open to unelect people, just as it also did not for the angels that have sinned. The only possibility of mercy that was created by the atoning work is that which was also guaranteed by the atoning work to be realised.
God has placed a moral obligation on all people, elect and unelect alike, to trust in Christ for forgiveness of their sins through His death. This moral obligation does not contradict the complete unavailability in actual substance of a channel of redemption to unelect people, since in God's design only elect people will be brought to obedience to this moral obligation.
Some context: In contrast to the above, it seems that some Reformed theologians hold a perspective something like as follows.
- One major and central facet of the atonement is that in Christ's death as a man, He died sacrificially as a representative of mankind before God, thereby purchasing the availability to all men and women of having their sins exchanged for His righteousness, if they will only repent and trust in Christ.
- Another important facet of the atonement is that when God in eternity past set His affection on all those whom He would in due course call to Himself, He designed that Christ would die as a propitiation to "buy their forgiveness" in the sense of buying for them the actuality that their sins are no longer held against them -- this forgiveness coming into effect through the repentance and faith in Christ that God in due course grants them.
(From listening to John Piper on the subject, and his discussion with Rick Warren on the subject, I expect that he would be roughly of this position and would not affirm all - perhaps not even any - of the four points further above.)
But it seems that many (perhaps more "traditional-minded") Reformed theologians find objectional any concept of payment for sin that involves purchasing the availability of forgiveness for people who will not ultimately be forgiven.
Accordingly, it seems that such theologians hold the notion of "actual atonement of the elect" to the strict exclusion of available atonement to everyone. Unlike John Piper, they seem to be fundamentally unable to say that "Christ died for all", without a contextual qualification of the word "all" to restrict it to only the elect.