Classical Rayleigh streaming is well known and can be modelled using Nyborg’s limiting velocity method as driven by fluid velocities adjacent to the walls parallel to the axis of the main acoustic resonance. We have demonstrated previously the existence and the mechanism of four-quadrant transducer plane streaming patterns in thin-layered acoustofluidic devices which are driven by the limiting velocities on the walls perpendicular to the axis of the main acoustic propagation. We have recently found experimentally that there is a third case which resembles Rayleigh streaming but is a more complex pattern related to three-dimensional cavity modes of an enclosure. This streaming has vortex sizes related to the effective wavelength in each cavity axis of the modes which can be much larger than those found in the one-dimensional case with Rayleigh streaming. We will call this here modal Rayleigh-like streaming and show that it can be important in layered acoustofluidic manipulation devices. This paper seeks to establish the conditions under which each of these is dominant and shows how the limiting velocity field for each relates to different parts of the complex acoustic intensity patterns at the driving boundaries.