Equity vs. Equality

Because we are living in a society where we have access to the same resources, does this make us as individuals equal? Or more to the point can we claim to live in an equitable society? Indeed, one persons position in an equal society can be a symbol of another's failure. Because I earn less than you, am I less successful? Because I come from a privileged background, is my success any less worthy?
The debate is even more poignant when opened up to health care. Indeed, in the UK we can almost speak of an equal and equitable health care system, until that is we cross the line into drugs pricing. While in the US, the equality on which the nation is built is a far distance from achieving equity in health care provision.