This is only a matter of terminology as both describe the production of syngas (H2 or CH4) as a primary product of organic valorization in aqeous processing. Gasification takes place beyond the critical point of water, where below that, liquid products have higher yields and gaseous products (mostly CO2) have between 5-20% yield.
In general, hydrothermal gasification is synonoymous with catalytic (slightly above the critical point) processing for a CH4 rich product, while supercritical water gasification is used for higher temperatures (500 and beyond celsius) for a primary product of H2. but again using the terminology vice versa would still be acceptable.