Atmospheric escape is loss of part or (virtually) all of a planet's atmosphere (the inverse of atmospheric retention). There are a number of mechanisms, all which are means by which the speed of gas molecules are boosted beyond the planet's escape velocity.
Generally, early in the life of a planet, a certain amount of escape occurs, which can virtually eliminate some constituents. Slower mechanisms may persist through the life of the planet. Over the long term, the outer portion of the atmosphere termed the exosphere is defined as a region where particle interactions are rare, meaning if a particle is given sufficient speed, it is unlikely to be slowed through another interaction, thus likely to escape. The exobase is the lowest level of this region.
Hydrodynamic escape is the atmosphere is simply not in hydrostatic equilibrium: pressure is such that the outer portion is pushed outwardly hard enough to escape. Given the gravity of the star, the Hill radius and Roche lobe are factors. The term blow off indicates very decided hydrodynamic escape, i.e., that can significantly reduce the atmosphere in a short amount of time. The term hydrodynamic escape is also used for the phenomenon of heavier molecules gaining sufficient speed and escaping due to repeated bumps by lighter molecules.
Thermal escape, i.e., due to temperature, includes Jeans escape, the escape of those molecules moving sufficiently fast, per the Maxwell-Boltzmann distribution. The term kinetic escape is sometimes used, kinetic energy underlying thermal energy. Mechanisms other than Jeans escape are sometimes included in the term thermal escape if temperature is a factor, including hydrodynamic escape.
The term non-thermal escape is used for other mechanisms, among them the influence of solar winds (or stellar winds, which can simply knock away molecules from the atmosphere, or on a larger scale, ram pressure) or impacts, and also of magnetic fields and ions. Ions in the atmosphere can be propelled out, possibly becoming neutral through charge exchange with another molecule along the way, or can bump (i.e., exchange kinetic energy) with neutral molecules. Another factor is EMR from the star, through photoionization, photodissociation, and photochemistry (from extreme ultraviolet and X-ray photons) which, in addition to producing ions, can result in less massive particles and also boost their individual speed, which in the exosphere may simply escape and through interaction can increase temperature, powering other escape mechanisms.
Smaller particles are more likely to escape: at a given temperature, their speed is faster, and in individual reactions, on a micro scale, they are more likely to gain sufficient speed by any of these means.
For the longer term escape mechanisms, the source of energy is of interest, e.g., EMR from the star. Core-driven escape is a term for escape powered by heat from within the planet, either primordial heat or from radioactive heating.
Diffusion-limited escape is atmospheric escape that is limited by the degree to which the escaping material diffuses upward through the atmosphere where other mechanisms can help it escape.