Define: Equality

Equality of humanity is a consternating nebulous concept that I can't seem to grasp. I'm all muddled up in phrases like 'deserving,' 'sacrifice,' 'standard,' etc. Additionally, I am at times disillusioned with experiences defined by moments: endless hours studying, seeing a sun-baked sitting lazy, ill-defined uses of agency, etc. With so many thrusting and competing ideas, what in the world does this phrase mean?:

All men are created equal

Every time I place my hand on my heart, I'm inadvertently reaffirming that phrase. When I watch fireworks and am compelled to sing 'God Bless America' I'm singing my truce with the American founders. I've lived and will most likely die on a soil that resounds equality, but I'm not sure I understand what it is.
Alma 1 contains some interesting guidelines concerning the ethical and spiritual dimensions of equality. The basis for interpretation is a people who 1. are immovable in keeping the commandments, 2. bore with patience the persecution which was heaped upon them, and 3. they labored with diligence, every man according to his strength. (First key: having freedom and equality doesn't mean one won't be persecuted)

Proper display of equality includes the responsibility of persons who have more to impart with persons who have less. The appropriate method of distribution is based on need only. Specifically, it is necessary to be liberal with all, having no respect to persons as to those who stand in need. Additionally, for crimes committed, every man must suffer according to that which he does (aka- moral responsibility).

Does such liberality conclude that we give based on need, not on status, social grace, or previous financial problems? Does this imply that if a man is sitting on the ground, holding a sign asking for money, potentially faking ineptitude, that we give because he has a need? Without reading in between the lines, I believe so.