No, it means you recognize that while they are equal to you, they are also different from you, and since they are different they should be treated differently (yet still with respect obviously).

Ah. Maybe since members of different groups are equal but different, they should get special facilities designed for these groups? Shall we call this "Some groups are more equal?" Or maybe "separate but equal?"

Again: Because everyone is different, treating them with equal respect requires treating them differently. This is not complicated.

People are different as individuals. They must be judged and treated accordingly as INDIVIDUALS. To treat them differently because of their group membership is to treat them unequally, even if you hop up and down and chant the mantra "equally!" forever.