Jean's Mass...is the quantity of mass needed for gravitational collapse to be triggered given the amount of internal thermal or magnetic support available in a cloud of gas.
Horizon mass...a somewhat vague and not frequently used concept which is roughly equal to the mass represented by a black hole event horizon of a given size. The Schwarschild radius = 2 G M/r c^2 where M is the black hole 'horizon' mass, and r is the radius of the black hole or horizon.
Damping mass....in the early history of the universe, gust after the so-called Recombination Era when the universe became transparent, one mass scales survived at 10^12 solar masses. This 'Damping mass' represent the scale over which photons were able to diffuse out of a density fluctuation and smooth it out or 'damp' it. The large scales can contain the photons better, and instead of being dissipated, these fluctuations continue to grow as the universe expands. After the universe became transparent, this diffusion process ended abruptly and the mass scale stopped growing at its final size of 1 trillion solar masses. After that time, it fragmented into individual galaxies. Damping mass, therefore, is a critical mass, below which scale density fluctuations are dissipated, and above which they grow.