A variety of processes cause interstellar gas to become cold enough and dense enough to form stars. On galactic scales, stellar instabilities, spiral waves, and global perturbations like bars can move the gas around supersonically and cause shocks to form that are larger than the characteristic size of a gravitational instability in the gas. Then giant cloud complexes form from the ambient gas. As these complexes dissipate their internal turbulent energy, they contract gravitationally and fragment because of converging and diverging turbulent motions until dense, thermally-dominated cold cloud cores form. Stellar pressures also compress the gas supersonically. On sufficiently large scales, these compressions lead to collapse in shells and rings. On small scales, stellar pressures can turn in pre-existing clumps unstable to collapse, especially along the edges of HII regions and super-bubbles.
The empirical laws of star formation have no obvious connection to the details of these triggering mechanisms. The empirical laws state mostly that star formation requires cold and dense gas. In the case of the Kennicutt (1998) law, with its non-linear dependence of star formation rate on total gas density, empirical evidence suggests also that general dynamical processes in the ISM are involved in determining the time scale. Since triggering on the length scale of these laws has the same dynamical time scale, all of the various triggering processes can mix together without much distinction.
The distinct contribution that triggering makes to the star formation rate might be most evident in large-scale regions where the average molecular fraction is neither very high nor very low. There the dynamical processes related to cloud formation could have a significant influence on the abundance of cold gas in clouds. There might still be a linear relation between cold gas mass and star formation rate at these places, because star formation follows cold gas no matter what forms the cold gas, but the rate of both cold gas formation and star formation could be modulated by dynamical processes more there than elsewhere.
The author is grateful to the National Science Foundation for support from grant AST-0707426, and to the conference organizers, particularly Professors Cristina Popescu and Richard Tuffs, for their support and hospitality.