A part of the problem, in my own opinion, is the aspect that the blood of the Cross of Christ paid for all time for all people the PENALTY of sin. It was not just "sufficient for all and effective for some" as some such sayings are used (by both arm and cal folks). John is expressly clear on this issue (1 John 2) and yet there are those who just want to limit the blood sacrifice.
However, the blood sacrifice, as totally complete for all humankind of all ages past, present and future, did not remove the need for atonement - in the Scriptures atonement means reconciliation.
There is no systematic scheme (other than heretical) that holds all folks will be saved and atonement is unlimited. How or to what degree the atonement is limited is highly contested on the Cal/Arm threads.
It is important to remember that mankind is always reconciled to God, God is never reconciled to mankind. God does not need to be reconciled to the world, but world to Him.
So what did the Father intend to do by sending His son to die for us?
What changed at Calvary?
First, the work of the Holy Spirit:
8 “And He, when He comes, will convict the world concerning sin and righteousness and judgment; 9 concerning sin, because they do not believe in Me; 10 and concerning righteousness, because I go to the Father and you no longer see Me; 11 and concerning judgment, because the ruler of this world has been judged.
Secondly, the indwelling and seal of the Holy Spirit - that presents us a "joint heirs" to the promise. Pre-Calvary, the Spirit would come and go. Saul had the Spirit then didn't have the Spirit. The Psalmist (51) begged God not remove the HS from him.
Thirdly, those who do not believe will spend eternity in the "second death" not because of sin, but because of unbelief. God has no record of atonement so he says, "depart from me, I never knew you" (John records that the believers will keep the commandments and attend to the needs of others as indicators of their belief). Remember John 3 and also recall the final judgment.
I saved one question for last, because (imo) it may be the most controversial.
"Did Jesus' death actually redeem anyone?"
Now many would impulsively say, "Certainly."
I say, "Nope."
The reason is the death is only ONE part of being redeemed. Death was not ownership. Not long ago, I made a purchase at a local home improvement center. I accidentally left behind one of the bags of purchased items. Later that week, I returned to the store and had to purchase the items again. Though they had already been purchased, and I had a receipt, and put them in a bag, I didn't claim ownership but left the items behind to be re-shelved. I had no true proof of ownership.
It was not enough for the blood of the pure lamb of God to be shed, but there must also be reconciliation - the atonement, the taking possession.
Not everyone is atoned, just as Christ stated - those that do not believe are already condemned. Such prefer darkness and do not come to the light, in fact they hate the light because light would show their deeds as evil.
Being sealed by the Holy Spirit is taking possession by God literally being in and living through us.
As you can see by this answer, I do not actually "fit" into either major "camp" without some modification to the standard thinking of that group.