I am having a difficult time trying to give words to an equivalence, namely, $\preceq$; for instance, how would I word $x \preceq y$? I know it's not that x is less than or equal to y, because $\preceq$ is just a generalization of different equivalences.
If $\preceq$ is some kind of order (partial or total) you can read $$x \preceq y$$
depending on context. Else, you might just read $x$ is in relation with $y$. Note that the code for this is