OK, here is the speech.
Starter, grower and layer are nutritional formulas for feed, differing for each age.
Crumbles, mash and pellets are the form of the feed, meaning the coarseness, or size of the pieces.
Team_realtree gave the age groups for the nutritonal formulas.
Most find they can only get certain makeups of these combinations locally. I can get layer in pellets or crumbles, for example. But I cannot get starter separate from grower; they only sell a combined starter/grower formula around here, and only in crumbles. So I buy starter/grower, and when they start to lay, I switch to layer pellets. I choose the pellets over the crumbles because they waste less.
There are other formulas out there, though they are not available here, so I haven't researched them. For example, Purina makes a flock raiser. Some companies make a finisher, I assume for meat birds, but again, I have not researched this.
One caveat: if you have baby chicks growing up with a hen or group of hens, you must feed starter or starter/grower, not layer. Reason is that the chicks will be harmed by the extra calcium in layer. If there are laying hens in with the chicks, you just offer chick feed, or starter, to all of them, and offer oyster shell separately, so the hens have the calcium they need available. The mama raising the chicks doesn't need this, though, as she will not lay while setting or raising chicks.
Does that make it clearer?
Here is a website that REALLY gets into the specifics of feeding, if you are interested:
http://www.lionsgrip.com/pastured.html