Both synthesis methods are performed in an autoclave which can bear high temperatures and pressures. However, in hydrothermal method the solution is aqueous (solvent is water), while in solvothermal method the solution is non-aqueous (solvent other than water). In the latter, the temperature is above the critical point of the solvent and therefore the pressure must be too high.
Hydrothermal synthesis refers to the synthesis through chemical reactions in an aqueous solution above the boiling point of water. While solvothermal synthesis is generally defined as a chemical reaction taking place in a solvent at temperatures above the boiling point and pressures above 1 bar. The medium used in a solvothermal synthesis can be anything from water (hydrothermal) to alcohol or any other organic or inorganic solvent.Hydrothermal and ionothermal are subcatagouries of solvothermal method.