The word "equality" is meaningless without the clarification: equality of what? Hair color? Penis size?
In the context of politics, the following two equalities are usually meant by the arguing sides — even when neither side makes their own meaning explicit:
Equality of Opportunity versus Equality of Results .
The "all men created equal" concept is about equality of opportunity: you start with (roughly) the same things as everybody else and whatever you achieve (or not achieve as the case might be) is due to your own industry, frugality, and, perhaps, genes. We might be created equal (subject to gene variations), but what we do after the creation is up to us.
The equality of results is the opposite: whatever you do, you will have (roughly) the same things at the end: if you are more successful than average, the State will tax you to ensure the results of the less successful aren't too different from yours — a concept lovingly referred to as "spreading the wealth around".
A large number of politicians made careers of conflating the two equalities — by harping at the absence of latter and implying, the former does not exist. Such demagoguery patently dishonest not only in theory, but also in practice...