Do different grades of leaded avgas differ in ways other than their lead content?
Gasoline (both avgas and mogas) grades are distinguished solely by octane rating and lead content.

In theory, the octane rating is the amount of actual octane (C8H18) it contains, with the remainder being mostly heptane (C7H16), hexane (C6H14), pentane (C5H12), etc. As you note, a higher octane rating is needed for engines with higher compression ratios.

A century ago, the only way to get high-octane gas was via distillation, and since actual octane is a tiny fraction of crude oil, this was very expensive. It was soon discovered, however, that adding TEL made gasoline behave like it had more octane than it actually did; the higher octane rating you needed, the more lead you added. Leaded gasoline was born, including the 80/87, 100/130 and 115/145 grades of avgas.

However, just a few decades later we discovered how to "crack" long-chain hydrocarbons into shorter ones. Cracking diesel produced (mostly) gasoline--and with a much higher fraction of octane than gasoline distilled directly from crude oil. This allowed creating a 100-octane grade of avgas without any lead, but some old engines actually need a little lead for other reasons, so 100LL was born.

In short, you can take any grade of unleaded gasoline and boost it to any higher grade just by adding enough lead. Start with a higher grade of unleaded, though, and you won't have to add as much.