There are many differences but with regard to the last three days, the hen knows what the egg is doing while the incubator hasn't got a clue. Around day 18 the eggs, or rather the developed chicks in the eggs talk to mum and mum talks back to the eggs. The chicks in the eggs talk to the other eggs (i'm using talk in the broadest possible sense). In fact there is communication going on at a level we don't really understand between the unhatched chicks and their mum. It's these communications that help the hen to try to control the hatch timings of her chicks. Ideally the hen wants the chicks to hatch in the tightest time segment she can manage so all the chicks develope at approximately the same rate. A hens natural instinct is to hatch and get the chicks off the nest and mobile as quickly as she can. She's particularly vunerable, as are the chicks during hatching.
No incubator can do this.
I've had hens get off the nest for a drink and a quick bath while chicks in her nest were hatching. I chewed my nails so badly I may have lost a bit of a fingertip on one or two.

It was hot at the nest site and most of the pipping had already taken place and the chicks were struggling to get free of their shells. Mums don't interfere with this in general I've found. They don't do assisted hatching.
Don't worry and let the hen do her thing. Most of all and possible very hard to do even after watching lots of hatchings is if mum leaves a chick part hatched, or even hatched but not mobile don't try and rescue it! After over twenty years of chickens I inadvetently did exactly the above. The chick was removed from the nest and spent two days in intensive care and then unexpectedly returned to me and slipped under mum one night. The chick survived. Mum accepted it. It's coming on for three months old and I've watched it every day and the chick is different. It was very slow to learn things the other three had down. It's still odd and if this had been a free range group I doubt the chick would have survived. It just didn't quite get the importance of keeping up with mum and it's those chicks that any predators are most likely to try for. Taking on mum is a serious risk for any predator; a chick on it's own, easy dinner.