There are many aspects which determine its various types.
Generally, number one below is the main answer to 'types of solution'.
1. Homogenous and heterogenous
2. Solid, liquid or gaseous
3. Saturated or unsaturated
Dilute, saturated, and super-saturated.
When the liquid contains as much of a solute as it can be the solute would precipitate out as a solid, it is saturated.
In some conditions of preparation solutions can be made that contain MORE solute than would normally be expected before precipitation. These are super-saturated solutions.
Usually, the addition of a nucleation point by addition of a crystal, or even a shock wave, will induce a rapid automatic precipitation of the excess solute.