I agree. T and U async with respect to each other means at least that T and U can be broken down into tasks t1, t2, t3, ... tn and u1, u2, ..., un, such that they can be interleaved in any order, but typically we still require that the t tasks are executed in sequential order. The divisions between the tasks are where they give up control, e.g. as they wait for data to be loaded into memory, or on a network call.

This is still a special case of what we mean by async wrt each other, because depending on the interleaving at each step and e.g. the data loaded into memory, the number of tasks may change, but the idea is that they still eventually terminate in a correct state.