What's the difference between hydrostatic force and bouyancy?

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Hydrostatic force refers to the pressure exerted by a fluid at rest, acting on all surfaces of an object submerged in the fluid. Buoyancy is the net upward force that results from the difference in hydrostatic pressure on the top and bottom surfaces of the submerged object. When a cube of wood is submerged in water, hydrostatic forces act on each face, but the buoyancy force is specifically the resultant vertical force that allows the object to float. Understanding the distinction between these two concepts is crucial for solving problems related to fluid mechanics. The relationship between hydrostatic force and buoyancy is fundamental in determining whether an object will sink or float in a fluid.
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If you submerge a cube of wood in water there are hydrostatic forces on all faces of the cube. The buoyancy force is the net vertical force produced by the hydrostatic forces.
 
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Nolsen said:

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What was your definition of hydrostatic force and of buoyancy?
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
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