Grit is used for your chickens' crop to help them digest food. Eggshells would help with a calcium level. If your using a calcium grit it would do both. I would not feed my chickens their own egg shells, as they will start breaking and eat their eggs. I give them oyster shells. Personally, i dont give my hens grit very often because i free range them and they will eat any small stones. Hopefully that helps
Eggshells are great to feed back to the hens for calcium, just crush them first, it will not teach them to eat their own eggs.
But,it isn't enough calcium for them, it would be best to also give them oyster shell on the side.
As to grit, oyster shell works a bit like grit... but not really, because it breaks down.
If they free range and have lots of dirt/sand/etc. they probably don't need grit on the side, they will find their own.
If however they don't have as much area to roam, or it freezes up (so the ground freezes hard with no more access to grit), then grit on the side is very helpful. They need the grit to properly digest their feed.
Great advice so far.
I only give my chicks,young birds grit for the most part, if there is a spell where I cannot let my bigger birds free range I will give them grit.
Free rangers find their own grit. Oyster shell is calcium as are eggshells so they don't quite work like grit. I feed mine their eggshells, I microwave them to cook anything on them and crush. No egg eaters here. If you have egg eating hens chances are there's something else they are missing and trying to get. I keep a dish of oyster shell out at all times, mostly for my rooster who is extra large fowl (Langshan) and needs the extra calcium. A good feed should have calcium supplemented in.
Many people will disagree with this, but since I give my birds some treats of seeds and grains I put some grit in their feeders along with some oyster shells. They take what they want. I used to put it in separate dishes but they always managed spill it and get it all over the floor and then wouldn't touch it.