To me, a << b also connotes that the inequality a < b is "robust". For example, even if we mismeasured the values of a and b quite severely, we'd likely still have a < b. Or perhaps later on in my mathematical argument I will consider values that are a bit larger than a, say 5*a. If I claimed before that a << b, it means the reader can be assured that I won't do anything to a that'll make it bigger than b.