The term hydrodynamic escape (or hydrodynamic gas loss) is used for thermal atmospheric escape in cases where electromagnetic radiation from the host star significantly heats the gas particles, often also resulting in photodissociation so the resulting smaller particles gain kinetic energy and are more likely to reach escape velocity or exceed the Roche lobe. The phenomena can also result in additional heavier molecules escaping due to the outward pressure. The distinction with Jeans escape is the latter is 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.
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.