What I wrote is just the most common distinction. There are certainly many deviations from this in literature. There is also an abundance of other tilde-derived symbols in mathematics, like ≅, ≅ or ≃. (I'm not really sure whether the first two signs are different. I thought they were when I copied them, but they look the same now. The first was supposed to have three straight bars and the second two. The last one has one straight bar.)