A lot depends on the manufacturer and what they call it so far as Starter/Grower/Layer/All-Ages/Flock Raiser/Game Bird etc goes, even feed called the same thing will vary to some extent.
What they call the sizes Mash/Crumbles/Pellet seems to be pretty standard, even if the size of the pellet or crumble will vary a little.
Except for Layer with the extra calcium most chicken foods are actually pretty darn similar and the biggest difference is the protein level.
Protein is money, so most more specialized feeds are made to have the lowest protein percentage possible and still have the chickens do well.
The 16% for your usual Layer seems to be where the cost of the feed is balanced out by the egg production in commercial operations.
Extra protein doesn't hurt most birds, and may actually help increase egg production and size, and it is good if they are molting or under stress etc. You do have to watch some big breeds and birds like Cornish X especially which can grow too fast, or layers, some of the commercial layers especially since they can have problems if pushed to mature too early.
Chick Starter is usually around 18-20% up to 24% protein and is usually formulated for growing chicks to about 8 weeks, but it can be fed to older birds. The 24% is usually used for turkeys and other game birds, though most people seem to like to feed them an even higher protein% with feeds made especially for them.
I actually feed a 20% chick starter that is made in pellet form by a local mill to all my birds, except young chicks which get chick starter in crumble form. I do cut the protein level down using grain to adolescent birds and some layers.
Grower/Finisher specifically is usually around 15%-16% protein and is for birds 8-18 weeks or so.
Layer is usually 15-17% but you can get higher, most commercial brands say for birds over 18 weeks. A lot of people do start to feed it until they chickens actually start to lay, especially breeds that are late starters. Other people never feed Layer, just feed one of the others and offer oyster shell on the side for the Layers.
All-Ages or Flock Raiser type foods are usually around 18% protein and can be fed to pretty much everything, just have oyster shell on the side for laying hens.
There are various Turkey feeds, Game Bird feeds, Conditioner Feeds etc, and those can have a lot higher protein% like 28-32%, if you want to up the protein% for your chickens because they are molting or something, these can be a good way to go.