The surfing hold down and freedive both involve holding your breath while submerged in water, but they have some key differences.

Freediving breath hold

Freediving breath hold is a deliberate and voluntary action where a diver takes a deep breath and holds it for an extended period while diving underwater to explore the depths of the ocean, interact with marine life or compete in breath-holding competitions. They are characterised by environmental control, diver readiness, states of deep relaxation and are heavily parasympathetic in nature.

The objective is to maximise bottom time, deepen and maintain relaxation, enhance safety, avoid blackouts, lung squeezes and complications that may arise from prolonged breath holding. Recover fully between times.

Surfing hold down

A surfing hold down, on the other hand, is an unintentional experience that occurs when a surfer has often been thrown from their board and violently penetrated the water under the full impact of the breaking wave. Resulting in a situation where they must unexpectedly perform repeated breath holds at the whim of the ocean. They are characterised by limited to nil environmental control, minimal to no preparation, high heart rate and stress and are heavily sympathetic.

The objective is to manage the stress and intensity, remain as calm as possible, conserve oxygen and energy and optimise very short and erratic breathing and recovery opportunities as they present.

How training varies between the two

In terms of training both require very different approaches in order to create specific and transferrable adaptations. For example. Surf training is characterised by multiple reps of high intensity short duration breath holds with limited recoveries with a focus on strengthening the respiratory system and tolerating extremely higher levels of CO2 and stress.

Whereas freedive training is characterised by less reps of low to moderate intensity long duration breath holds with long recovery times and a focus on obtaining and maintaining a state deep relaxation. Adaptations sought is more a tolerance to hypoxia and reduction of CO2 sensitivity (increase in CO2 thresh hold set point).
Overall, while both freediving and surfing involve holding your breath underwater, the circumstances and objectives differ significantly, and the techniques for training vary accordingly.