Dont think you are right. At least for A LOT of people that I've met, equality means treating things, people the same. Sometimes its fans of the idea and sometimes its opponents of the idea but most of the time there is a consensus on that.
The job market is a good topic to bring up, I'll see if I can find a video that I watched a whiles back which does make reference to that:
I dont agree with the framing of the idea of equality in this video but it illustrates the point, I also dont like the kind of discussion of a social justice movement too as I dont find there is a movement and social justice itself is much, much more ill defined by its supporters and detractors than equality even is.
OK, so, I'll expect abreactions to the title of the video, the guys talking in it, whatever, but listen to the story about the guards in the whitehouse. This is a very good example of mistakes arising from a serious treatment of equality as sameness.
I've also encountered myself, a lot of times, the problems that arise from situations in which everyone is treated the same with the exact same expectations of people and it results in the more skilled, experienced etc. people carrying the can, they could be cheerful about it or they could be storing up problems for themselves but it'll be the reality and unfortunately I've also seen how seriously gendered things can be too.