Relentless Rage allows you to avoid passing out with a successful Constitution saving throw.
Starting at 11th level, your rage can keep you fighting despite grievous wounds. If you drop to 0 hit points while you're raging and don't die outright, you can make a DC 10 Constitution saving throw. If you succeed, you drop to 1 hit point instead.
A Half-Orc's Relentless Endurance allows you to do the same.
When you are reduced to 0 hit points but not killed outright, you can drop to 1 hit point instead. You can't use this feature again until you finish a long rest.
As a Half-Orc Barbarian, after failing to come back to 1 hit point using your Relentless Rage can you immediately try to do the same using Relentless Endurance?