Hydrodynamic escape (or Hydrodynamic gas loss) is atmospheric escape when conditions are far from hydrostatic equilibrium, i.e., the atmosphere is dynamic, losing gas rapidly, due to a significant portion of the molecules moving above escape velocity, or "settling" sufficiently high that the gravity of another body dominates (i.e., beyond the Hill radius or reaching a Roche lobe). Lighter molecules always reach a faster average speed when molecules bump each other, and more of them will have sufficient speed to escape, and hydrogen is lightest and most readily escapes. Jeans escape is the case when just a tiny fraction of the molecules are moving sufficiently fast to escape, in which case atmosphere can be viewed as nearly stable but with a slow leak. But with the right combination of temperature, pressure and gravity, the light molecules are escaping in bulk, i.e., hydrodynamic escape. The temperature must be sufficiently high and hydrodynamic escape is classified as a type of thermal escape. Often a factor on bodies (such as planets or moons) is high-energy photons from the host star (such as XEUV) heating the outer atmosphere.
Blowoff refers to the fact that hydrodynamic escape of hydrogen often carries some heavier molecules along with it: so many hydrogen molecules are moving upward that other molecules can receive a significant push in that direction. This phenomena has been explored theoretically as a means by which some bodies lose some compounds early on that would otherwise remain. When the term hydrodynamic escape is used, this kind of blowoff is sometimes the phenomenon of interest.
The phrase hydrodynamic escape may sometimes be considered to encompass Jeans escape as well, so read with care.