Short answers, pulled from the story.
Lamb is meat from sheep in their first year of life; hogget comes from sheep in their second year; mutton is meat from older sheep with more than two permanent incisor teeth in wear. Mutton has a stronger flavour and tougher texture than lamb because it contains a higher concentration of species-characteristic fatty acids and more mature connective tissue.
In most countries of South Asia, the word "mutton" is applied to goat meat by long-standing local convention, not confusion. The domestic sheep population on the Indian subcontinent has been declining for over 40 years, leaving goat as the dominant red meat sold under that label.
Abbacchio is an unweaned or recently weaned lamb in the Romanesco dialect, distinct from agnello, which refers to a lamb nearly a year old that has already been shorn twice. The European Union has awarded abbacchio Protected Geographical Indication status, recognising it as a traditional product of the Lazio region where around 100 recipes for preparing it developed over the centuries.
Mongolia is the largest per-capita consumer of sheep meat overall, at 45.1 kilograms per person according to the OECD-FAO Agricultural Outlook for 2016, based on 2015 data. Among EU nations, Greece leads with 12.3 kilograms per capita, while average per-capita consumption in the United States is only 400 grams per year.
Salt marsh lamb, also called agneau de pre-sale in French, comes from sheep that graze on coastal estuaries washed by tides where salt-tolerant plants like samphire, sorrel, and sea lavender grow. In the United Kingdom it is reared at sites including Harlech and the Gower Peninsula in Wales, the Somerset Levels, Morecambe Bay, and the Solway Firth.
Western Kentucky was a strong wool-producing region, which left a steady supply of older sheep whose meat needed to be used. Older animals with tougher flesh respond well to long, slow pit cooking, and the local barbecue tradition grew directly from that practical need. Owensboro, Kentucky, is specifically identified as a centre of this specialty.