On a multi-airline itinerary the allowance that governs your bag is often not the airline whose aircraft you board. This works out which rule actually applies.
On a multi-airline itinerary the allowance that governs your bag is often not the airline whose aircraft you board. Add your legs and this works out the rule that actually applies, and the strictest limit across the whole trip.
One ticket usually means a single allowance applies across the whole journey. Separate tickets mean each airline charges its own, and you may have to reclaim and recheck your bag.
When one ticket covers flights on more than one airline, a single baggage allowance normally applies to the whole journey — and it is set by the Most Significant Carrier, not by whichever airline you happen to be flying on a given leg.
The Most Significant Carrier is, broadly, the airline operating the longest or most significant international sector of your itinerary. Its allowance follows your bag from origin to final destination, including on legs flown by other carriers. This is why a passenger flying a generous long-haul carrier into a strict regional one keeps the generous allowance, and why the reverse also holds and costs people money.
Everything above depends on a single ticket. Two separate bookings are two separate contracts: each airline applies its own allowance, charges its own fees, and has no obligation to your onward flight. You will usually have to clear immigration, collect your bag and check in again — and if the first flight is late, the second airline owes you nothing.
The saving on separate tickets is real. So is the risk. Know which one you have booked.
Your ticket confirmation states the baggage allowance that was actually applied at the moment of booking. That wording, not a website table, is what the check-in desk goes by. If it disagrees with what you expected, sort it out before you get to the airport.