It depends on the author/field. In analysis sometimes f(n) <<g(n) means f(n) = o(g(n)), but other times (especially in discrete math) f(n) << g(n) means f(n) = O(g(n)).

Due to this ambiguity, I think the notation

f(n) ~< g(n) or in latex f(n) \lesssim g(n) is more clear