The real world provides us with a nice test case to examine whether egalitarians are motivated by envy or a desire to help the poor.
If they were motivated by envy, then if they get rich, we'd expect them to live large and find excuses for their own behavior.
If they were motivated by a desire to help the poor, then if they get rich, we'd expect them to donate lots of money to help the poor.
What we overwhelmingly see among egalitarians is the former, not the latter. That's the opposite of what we see among utilitarians, who generally seem to mean what they say.
Egalitarians of course have plenty of rationalization strategies to excuse their behavior, but none of them work, as Chris and I show here.