Self transfer can mean so many things in different scenarios. If you book a ticket through third party, you are responsible for managing everything including luggage shift, re-check in, time management, flight delays etc. On the other hand, if you book directly through the airlines website, the options that you see are based on the association that they have with their partner airlines. For example, we flew from Hyd to JFK last summer. The direct flight from India to JFK is from Mumbai. So what they are doing right now is to pool people from different hubs to Mumbai and then get them on to the final flight. Not sure if it was because we were flying business, but they handled everything. There was flight delay from Hyd (Vistara) but we didn't need to bother. No luggage checkout and checking again. They also fast tracked us through all security checkpoints and got us on to final flight. Hope this helps.!