The US is rather in the dark ages with lamb labeling, as it's not as widely popular here as it is in Europe. Lamb popularity, though, continues to rise as we have obviously more immigration and secondly that sheep are more environmentally friendly to raise than cattle.
Here is how it works in the US:
1) Up to 1 year old it is a lamb; unless
2) It has its first set of permanent teeth in place (which would be 1 pair of teeth, or two teeth).
3) There is no definition of "mutton" or "hogget" for the USDA. So, when you sell commercially and apply for labeling, you really can only label something as lamb. So, on packged food (think your lamb and rice dogfood), everything is called lamb if it comes from sheep.
Does this strike you as stupid? Yes, me too.
Here is how it really works in countries where sheep are eaten in great numbers (my wife is from North Yorkshire, my mom from Herefordshire and my nanna from Worcestershire):
1) A lamb is a lamb as long as it has its milk teeth. At some point right around a year old (either sooner, or later depending on the season it was born), these teeth are replace by the first pair of permanent teeth.
2) An animal over 1 year old but younger than 2 is known as "hogget", or in some places "fat lamb".
I raise, market and eat a lot of hogget. I prefer hogget. The cuts are larger than in lamb, you get far more meat per carcass and I think the flavor is better than lamb. I have customers who get hoggets from me. Now, I can't "label" it hogget on a USDA approved label, but I market and sell it.
Too me, eating an 80 lb lamb (live weight) is simply wasteful. They are far better at 110# lbs live weight.
Another advantage of hogget is this allows you to retain all your ewe lambs. Then, come the following year they should be lambing right at 1 year old. If they don't drop a lamb, then they go straight into the hogget marketing (the wethers are all eaten as lambs in Fall).
3) Mutton, then, would be anything beyond hogget or fat lamb.. so 2+ years old. These are almost always cull ewes with broken mouth (over 5 years old). Persoanlly, I like mutton. I don't think there is a difference in taste really.
I think because people are scared to eat lamb, they're terrified by teh full flavor of mutton.
4) There is an "old butcher's tale" that they snap the foreshank. If it breaks at the wrist it's a lamb, if it breaks at the bone it's older. I have NEVER been able to find an objective account of where this is used, though. And I may have it backwards even.
I lamb in May, it's late for most, but ideal for me. I will call it all lamb until next April when they are shipped for sale at my farm market. They are up to 125# live weight by then; but it's still lamb.
The 'strange' thing for most people is that sheep are still commonly grass fed and grass finished. A grass fed animal has a totally different flavor than a grain finished one. Most people learn to crave it, others can't get over it because they believe Safeway who claims a corn finished beast is better. The bottom line is cows and sheep are designed to turn grass into meat. You absolutely do not need to grain them. I market grass fed, grass finished lamb, and I have customers who drive 2 hours to get it.