A2 is an air hardening steel- what the A stands for, and while having the same amount of carbon has more alloying elements. These alloying elements lead to carbide formation which in turn is intended to increase edge retention by resisting wear.
PMV is a powder metallurgy steel - what the pm stands for, and is even more alloyed than A2. By using the PM process you can pack a load of alloying if compounds in, get them evenly distributed and use massive pressure to avoid grain growth. It’s more complex than that, and there are books written on it if you want to google.
The offset of the carbides is that it takes a bit longer to sharpen, there’s a debate raging about the need to use diamonds to cut the carbides to sharpen effectively, and they make the steel less tough so more prone to edge failure through chipping.
O1 being the least alloyed will be quick to sharpen, take a keen edge, but not hood it as long.
The reason to pick one of the other would be if you want a steel that gets sharp easily but needs regular touch ups- pick O1, if you’re happy working with a slightly fuller edge that’ll last longer and you don’t mind the odd chip- pick A2. You work with a lot of hard abrasive timbers that dull blades quickly - pick PMV.
If picking between planes - PMV for a Jack, O1 for a smoother.
I could write more but it gets detailed and dull quickly