I have already apologised for my inexplicable (even to myself

) use of the term "Particular Atonement". However, I did give the example of the "Particular Baptist" and "General Baptist" groupings, which was based on what each group held about Particular Redemption.
Spurgeon preached a sermon entitled "Particular Redemption", which started (emphasis mine):
I begin this morning with the doctrine of Redemption. "He gave his life a ransom for many."
The doctrine of Redemption is one of the most important doctrines of the system of faith. A mistake on this point will inevitably lead to a mistake through the entire system of our belief.
Now, you are aware that there are different theories of Redemption. All Christians hold that Christ died to redeem, but all Christians do not teach the same redemption. We differ as to the nature of atonement, and as to the design of redemption. For instance, the Arminian holds that Christ, when He died, did not die with an intent to save any particular person; and they teach that Christ's death does not in itself secure, beyond doubt, the salvation of any one man living. They believe that Christ died to make the salvation of all men possible, or that by the doing of something else, any man who pleases may attain unto eternal life; consequently, they are obliged to hold that if man's will would not give way and voluntarily surrender to grace, then Christ's atonement would be unavailing. They hold that there was no particularity and speciality in the death of Christ. Christ died, according to them, as much for Judas in Hell as for Peter who mounted to Heaven. They believe that for those who are consigned to eternal fire, there was a true and real a redemption made as for those who now stand before the throne of the Most High. Now, we believe no such thing. We hold that Christ, when He died, had an object in view, and that object will most assuredly, and beyond a doubt, be accomplished.
The whole sermon can be read at:
http://www.spurgeon.org/sermons/0181.htm
I also came across this, about Wesley, Whitefield and Methodism, which also seems to use the term "Particular Redemption" differently to you:
Wesley's Arminianism caused an estrangement from the uncompromising Calvinist Whitefield. When controversy had become intense, Wesley summed up by saying that "those who believed in universal redemption had no desire to separate, but that those who held particular redemption would not hear of any accommodation, being determined to have no fellowship with men who were in such dangerous errors; so there were now two sorts of Methodists-those for particular and those for general redemption." The break between Wesley and Whitefield lasted but a short time, but the result was the formation of two sorts of organized Methodists, "Wesleyan Methodists" and "Calvinistic Methodists."
From:
http://www.ccel.org/s/schaff/encyc/encyc07/htm/ii.xi.ii.htm
I am sure others will correct me if I am mistaken, but (as I understand it) the term "Particular Redemption" does not mean that Christ died to make everyone's salvation possible, but only redeemed those who believe on Him.