Layer feed, which I think it what most people would consider "grown up" feed is just chicken feed with more calcium and usually slightly less protein. It is designed to be complete nutrition for laying hens and laying hens only. It is not for young birds, roosters or birds that are not laying for any reason (age, breed, season, molting, etc). It is especially not good for young birds.
You have several options when feeding your birds. Many people feed a starter (medicated or non, your choice) for 8 weeks or so then which to a grower (if you feed a non-medicated starter you can probably skip this step and just stick with your starter) then around 20 weeks or when the birds start laying they switch to a layer. If you have all hens of the same age this will work fine. I do think it is important to understand though that a layer feed does not make birds lay it just has extra calcium that they need to make egg shells. There are alternative ways to give them this pcalcium if you choose.
I personally feed a grower (organic, soy-free 20% protein) to all of my birds at all life stages and never switch to a layer. I do this because I have a small mixed flock with birds of different ages and also have some breeds that do not lay as regularly. I feed the grower and put a bowl of oyster shell as a calcium source separate on the side. If the calcium is on the side and not mixed into the feed (like it is in a layer feed) then the birds will only eat it as needed. So, young birds and roos who need less calcium will eat much less and your laying hens will eat more. When my birds go into molt they stop eating it (If I were feeding layer they wouldn't have this option).
I also choose this feed because it has the animal protein that I prefer for them and is organic and has a higher protein that let's me supplement their feed with a fodder mix that saves me a little money and adds healthy greens to their diet without effecting their balance of nutrition.
Some people will feed laying during the summer high production months and then switch to a grower or flock raiser in the winter in the lower production months.
Feed bags have ages on them as a guide but it is not a rule. I think it is good to understand the different kinds so you can decide what works best with your flock and your farming goals. It seems sort of complicated at first but really comes down to what kind of ingredients you want your feed to have and deciding where you laying hens will get their calcium.
Meat specific breeds are a different story with a different feeding schedule if your ever decide to go down that path.