They are very different processes. Vapor smoothing is more of a hack than anything. It traps the solvent in the part for a very long time. Like using acetone on auto body trim and bumpers that are mostly ABS will get you fired from any shop. It will bleed and ruin the top coat an clear coat as it vents from underneath them. In my testing, acetone greatly alters the structural strength as well. Polishing maintains or in some cases improves the mechanical performance of parts. Even for cosmetics, the polished part will look like it was injection molded while the inconsistency and rounded corners of vapor smoothing look very DIY. Polishing can be done poorly, and I am an actual finishing pro, so YRMV.

I'm having trouble finding any of the places I described it in my post history. I thought I made an early post in this community about polishing, but I don't see it. This has a couple of examples: https://lemmy.world/post/105150 but they are not great shots or anything.

I owned a small auto body shop through most of my 20's. That is where I am drawing my experience from. I am using a similar technique as one might use to clear plastic headlights. With PLA you just need to be careful about overheating. It isn't hard. You just start with something like 240 grit and step to, 400, 600, 800, 1200, 2000, then use a heavy cut compound to go into a shine, and a finishing compound if you want a full gloss. The most time is spent on the first grit. Every inclusion should be removed. It helps to tune the print to avoid any inclusions by very slight over extrusion. PLA can make a smooth solid looking surface pretty easily. Each grit must completely remove all scratches from the last grit. When a person is not familiar with how much work this involves for each step, use a guide coat. This can be a dusting of spray paint, or scribbling with a graphite pencil all over the surface. Then you sand the surface until all guide coat marks are gone. Consumer polishing compounds in the US targeted for automotive are worthless crap. In the professional space 3M Perfect-It 2 is the standard or was when I was painting. Toothpaste is a better polishing compound than anything you can buy in a big box or auto parts store. It will take a long time, but you do not need a mechanical polishing setup. Get a rag that has a similar texture to a cheap crew sock, spend an evening watching TV for a few hours, and never stop rubbing the thing with the sock and compound/toothpaste at the texture of something like playdough or a block of clay. Compounds are like lubricant while the texture of the pad/rag is doing the work. The golden rule of auto body finishing is "when you think you should be done, take a break because you're half way done."