Both Star Alliance and oneworld cap you at 16 segments, and connections count against that total, not just the cities you stop in. Both also require you to cross the Atlantic and the Pacific exactly once each, so you cannot cross the same ocean twice even where it would make geographic sense.
Both Star Alliance and oneworld cap a round-the-world ticket at 16 segments. That sounds generous until you realise connections count as segments, not just the cities you actually stop in. A routing from New York to London to Nairobi burns two segments for what feels like one destination.
Two more rules trip people up. Surface sectors, where you travel overland between two cities and pick up your next flight elsewhere, are permitted but count against your segment or mileage allowance differently depending on the alliance. And both alliances require you to cross the Atlantic exactly once and the Pacific exactly once. You cannot cross the same ocean twice, even where it would make obvious geographic sense for your trip.
On Star Alliance there is a second budget running alongside the segment count: total mileage, in tiers at 26,000, 29,000, 34,000 and 39,000 miles. Every segment burns mileage, so a short side trip from Bangkok to Bali and back eats into the cap even though the flights are short. Oneworld prices by continents visited instead, which is simpler to follow but can cost more if you only touch a continent briefly.