What are the primary breathing apparatuses for scuba

Context: Breathing apparatus
Main article: Scuba set

Recreational diver putting on his scuba set before diving
The defining equipment used by a scuba diver is the eponymous scuba, the self-contained underwater breathing apparatus which allows the diver to breathe while diving, and is transported by the diver. It is also commonly referred to as the scuba set.

As one descends, in addition to the normal atmospheric pressure at the surface, the water exerts increasing hydrostatic pressure of approximately 1 bar for every 10 m of depth. The pressure of the inhaled breath must balance the surrounding or ambient pressure to allow controlled inflation of the lungs. It becomes virtually impossible to breathe air at normal atmospheric pressure through a tube below three feet under the water.

Most recreational scuba diving is done using a half mask which covers the diver's eyes and nose, and a mouthpiece to supply the breathing gas from the demand valve or rebreather. Inhaling from a regulator's mouthpiece becomes second nature very quickly. The other common arrangement is a full face mask which covers the eyes, nose and mouth, and often allows the diver to breathe through the nose. Professional scuba divers are more likely to use full face masks, which protect the diver's airway if the diver loses consciousness.

Open-circuit
Main article: Diving regulator

Aqualung Legend second stage regulator

Aqualung first stage regulator

Gekko dive computer with attached pressure gauge and compass

Suunto submersible pressure gauge display
Open circuit scuba has no provision for using the breathing gas more than once for respiration. The gas inhaled from the scuba equipment is exhaled to the environment, or occasionally into another item of equipment for a special purpose, usually to increase the buoyancy of a lifting device such as a buoyancy compensator, inflatable surface marker buoy or small lifting bag. The breathing gas is generally provided from a high-pressure diving cylinder through a scuba regulator. By always providing the appropriate breathing gas at ambient pressure, demand valve regulators ensure the diver can inhale and exhale naturally and without excessive effort, regardless of depth, as and when needed.

The most commonly used scuba set uses a "single-hose" open circuit 2-stage demand regulator, connected to a single back-mounted high-pressure gas cylinder, with the first stage connected to the cylinder valve and the second stage at the mouthpiece. This arrangement differs from Émile Gagnan's and Jacques Cousteau's original 1942 "twin-hose" design, known as the Aqua-lung, in which the cylinder pressure was reduced to ambient pressure in one or two stages which were all in the housing mounted to the cylinder valve or manifold. The "single-hose" system has significant advantages over the original system for most applications.

In the "single-hose" two-stage design, the first stage regulator reduces the cylinder pressure of up to about 300 bars to an intermediate pressure of about 8 to 10 bars above ambient pressure. The second stage demand valve regulator, supplied by a low-pressure hose from the first stage, delivers the breathing gas at ambient pressure to the diver's mouth. The exhaled gases are exhausted directly to the environment as waste through a non-return valve on the second stage housing. The first stage typically has at least one outlet port delivering gas at full tank pressure which is connected to the diver's submersible pressure gauge or dive computer, to show how much breathing gas remains in the cylinder.

Rebreather

An Inspiration electronic fully closed circuit rebreather
Main article: Diving rebreather
Less common are closed circuit and semi-closed rebreathers which, unlike open-circuit sets that vent off all exhaled gases, process all or part of each exhaled breath for re-use by removing the carbon dioxide and replacing the oxygen used by the diver. Rebreathers release few or no gas bubbles into the water, and use much less stored gas volume, for an equivalent depth and time because exhaled oxygen is recovered; this has advantages for research, military, photography, and other applications. Rebreathers are more complex and more expensive than open-circuit scuba, and special training and correct maintenance are required for them to be safely used, due to the larger variety of potential failure modes.

In a closed-circuit rebreather the oxygen partial pressure in the rebreather is controlled, so it can be maintained at a safe continuous maximum, which reduces the inert gas partial pressure in the breathing loop. Minimising the inert gas loading of the diver's tissues for a given dive profile reduces the decompression obligation. This requires continuous monitoring of actual partial pressures with time and for maximum effectiveness requires real-time computer processing by the diver's decompression computer. Decompression can be much reduced compared to fixed ratio gas mixes used in other scuba systems and, as a result, divers can stay down longer or require less time to decompress. A semi-closed circuit rebreather injects a constant mass flow of a fixed breathing gas mixture into the breathing loop, or replaces a specific percentage of the respired volume, so the partial pressure of oxygen at any time during the dive depends on the diver's oxygen consumption and/or breathing rate. Planning decompression requirements requires a more conservative approach for a SCR than for a CCR, but decompression computers with a real-time oxygen partial pressure input can optimise decompression for these systems. Because rebreathers produce very few bubbles, they do not disturb marine life or make a diver's presence known at the surface; this is useful for underwater photography, and for covert work.

Answer: The most common breathing apparatus for Scuba Diving is an open circuit single hose 2-stage demand regulator connected to a single gas cylinder.  A less common apparatus is a Closed Circuit or Semi-Closed rebreather.