Squish- mixture motion caused by "squishing" the mixture out of the tight space between piston and head. Encourages shorter burn time which means more power and less tendency for spark knock.
Quench- mixture cooling "quenching" in close proximity to piston top and head. Spark knock happens in the end gas (last portion of the mixture to burn). Cooling the end gas reduces tendency for spark knock.
Two totally different effects, both good, from a tight space between piston top and head surface.
Fuel/air mixtures start to react (precursor reactions) as temperature and pressure rises but before actually burning. If the reactions proceed too far before burning, the mixture will spontaneously ignite. This is spark knock. Faster burn means less time for precursor reactions, cooler end gas means slower precursor reactions, both reduce tendency for spark knock.
