Non-Catholic here. What you describe here sounds like what the Bible calls The Judgement Seat of Christ. That is, the judgement of a believers works, not their salvation. All those whose names are found in The Lamb's Book of Life (believer's in Jesus Christ) will be at this judgement. Our works which were of the wrong motive (for example), will be burned up & what is left (good works) will earn us rewards in heaven.
On the other hand, those who reject Christ will be at The Great White Throne Judgement. Here. each person will be shown that their name IS NOT in The Lamb's Book of Life, & they will be thrown into the Lake of Fire for eternity.
Essentially, this is correct. As I mentioned in my post - you CANNOT go to Hell from Purgatory, only heaven. You are saved.
In general, however, Catholic thought tends to support the idea that all the saved experience Purgatory of some sort or degree - no one gets to go to Heaven and proudly (in the words of Peter Gabriel) "walk through the front door".
The concepts are essentially the same (perhaps some minor differences if we really sat down and analyzed every specific detail) - only with different terms.
Practicing Catholic here. Limbo is no longer taught or talked about in the Church.
Purgatory is still being taught and talked about. It is mentioned at every single mass. We always pray for the souls in Purgatory at each Mass.
All Souls Day - A special day to pray and give Mass for the souls in Purgatory.
This is likely where some of the confusion comes into play - Purgatory is now though of like a place - and we are praying for the souls that are in Purgatory - now we get a sense that they have been (and are going to be) there for a while.
Better to say that we pray for the souls who are in the state of Purgatory - and, in fact, there is no time in Purgatory, so it's hard to even think of praying for the souls there.
This is why God is thought of as being atemporal. The soul of our loved one after they die - is not experiencing purgatory in our timeframe - yet we can pray for them, since God is also "outside" our timeframe, any prayer He hears can be acted upon in an atemporal manner.
Basically, when we pray for souls in Purgatory, we are asking God to have mercy upon them - i.e. go easy on them, please. Our prayers occur in linear time, but are being heard in the atemporal afterlife. So, we can keep on praying for any soul in purgatory, even though there is no way for us to comprehend the fact that their experience took no time from our perspective.
I'm sorry, this is a terribly confusing topic - the human limitations on language mean that we just can't explain atemporality all that well. Plus, not having experienced it, it's kind of hard to get a good frame of reference to build upon.
I hope I haven't confused things further.