Depends on the breed and the feeding!
if its a commercial breed (big, white, usually ugly!) then you can get them to slaughter weight in under 6 months ie they go off the same year they are born. But if sold as stores that would imply they need a few more months of good grass so maybe later in the year,
Traditional breeds like Shetland/Hebridean etc can be sent off their first winter at about 9 months. But ideally they go off as hoggett ie in their second year.
So if you were drawing a distinction between young lamb and more mature hoggett or mutton, the commercial breeds would make more sense for the former (they get to a commercial killing size in the first summer) and the trad breeds more sense for hoggett or older (mutton) as they can overwinter on a lot less in the way of pampering, just hay and a lick for the most part.
There isnt a different nature of product in terms of cuts like there is in pigs (where the breeds are often better for one or the other of bacon or pork too), but you can choose slightly different cuts eg with hoggett or mutton you might be havign that as you want to do more long /slow cooking (which mutton might need; trad breed hoggett doesnt but it can stand up to it and amazing taste!), so eg you might remove the shanks from the joints so you can do slow cooked lamb shanks.
Strongly recommend the River Cottage diagram of all the possible joints in their Meat book, (you can buy it as a small poster too). It helps a lot to work out the overlapping names of joints so you dont end up ordering a joint where you have already used up that part of the animal between two othr joints!