Apnea = no breathing (transient cessation of breathing... hopefully transient... the other alternative... known as respiratory arrest (ie. you permanently stop breathing)... is not good).  You could use this term to describe "breath holding."

Apneustic breathing pattern = periods of no breathing interrupted by inspiratory gasps

Asphyxiation = sufficient O₂ is not available to support cells, for any reason

Cyanotic/cyanosis = blue tinged tissues due to excessive buildup of carbaminohemoglobin (excess CO₂)... generally accompanies hypoxia

Dyspnea = difficult, painful, or labored breathing

Eupnea = tentatively normal breathing (quiet, normal, resting breathing)

Hypercapnia and Hypercarbia = same thing; increased PCO₂ in the blood (generally arterial)

Hyperpnea = increased ventilation - increased tidal volume (depth of respiration) with or without increased respiration rate, with increased metabolic demands (eg. with exercise)

Hypocapnia or hypocarbia = decreased PCO₂ in the blood (generally arterial)

Hypoventilation = can be a change in rate, depth or both, resulting in a decrease in the overall volume of air moved in and out of the lungs per unit of time (generally results in increased blood CO₂ tension).

Hypoxia = lowered O₂ tension in the tissues

Hyperventilation = can be a change in rate, depth or both, resulting in an increase in the overall volume of aire moved in and out of the lungs per unit of time (generally results in reduced blood CO₂ tension)

Tachypnea = increased rate of breathing (abnormal situation leading to increased ventilation rate)

Polypnea = synonymous with panting (as in dogs)

Suffocation = lack of O₂ due to factor(s) preventing ventilation

Tachypnea and Polypnea are technically similar, but in the strictest clinical sense, polypnea is used to mean panting, and so is used more frequently in veterinary science than in human health sciences (panting is increased respiration rate, usually associated with an attempt to lose excess heat).  Tachypnea means rate of respiration has increased above normal.

Figure: Cheyne-Stokes Breathing

Cheyne-Stokes refers to periods of apnea interrupted by periods of increasing and decreasing tidal volume.  One cause of Cheyne-Stokes patterns is severe hypoxemia.  Sometimes Cheyne-Stokes breathing patterns precede death.