The interstellar medium (ISM) is, as you say, the gas (and dust) in between the stars, within a galaxy. It consists of molecular, neutral and ionized gas, with densities ranging from $\sim 10^{-3}$ to $\sim 10^{6}$ particles per cm$^{3}$ and temperatures ranging from a few K up to 10,000 or 20,000 K. The molecular gas is the coldest and densest, usually found in molecular clouds.

The intergalactic medium (IGM) is the gas (and small amounts of dust) in between galaxies. It is mostly ionized gas with densities $\sim 10^{-6}$ particles per cm$^{3}$ and temperatures ranging from $\sim 10^{5}$ to $\sim 10^{7}$ K. Due to this temperature range, it is sometimes referred to as the "warm-hot" intergalactic medium. There is, however, evidence for some regions of neutral hydrogen with temperatures of $\sim 10^{4}$ K.

The intracluster medium is a subset of the IGM that makes up the IGM inside galaxy clusters (in between the galaxies in the cluster). This means that it is somewhat denser than the general IGM (densities of $\sim 10^{-3}$ per cm$^{3}$, denser towards the centers of clusters) and hotter as well, with temperatures of $\sim 10^{7}$ to as much as $10^{8}$ K.