Final answer:
Sugar operons like the lac operon are named after the sugars they help metabolize and are typically off by default, while amino acid operons like the trp operon are named after the amino acids they synthesize and are usually on by default.
Step-by-step explanation:
The primary differences between how sugar operons like the lac operon and amino acid operons such as the trp operon are named lies in the substances they regulate and their default states of operation. The lac operon's naming indicates it regulates lactose metabolism, and it remains off by default because lactose is not always present in the environment. Conversely, the trp operon is named for tryptophan, an amino acid, and is normally in the 'on' state, as tryptophan synthesis is typically essential for the cell.
Sugar operons often control genes for enzymes that break down sugars, which are external to the cell and not always available; thus, these operons like the lac operon are contingent on the sugar's presence. In contrast, amino acid operons such as the His, Leu, and Ara operons are often related to the synthesis of essential cellular substances like amino acids and are generally operated based on the internal biosynthetic demand of the cell.