Reading this description of cyanide poisoning — http://indianapublicmedia.org/amomentofscience/how-cyanide-kills/ — makes me wonder if death by cyanide is equivalent to suffocation. Is it?
In suffocation or asphyxiation you are actually deprived of breathing oxygen. As a result, the arterial blood oxygen concentration decreases (hypoxemia) which is detected by the chemoreceptors of the carotid body and aortic arch. This induces a neuronal response in the medulla that increases the respiratory rate. Simply put, you get panicked. Prolonged suffocation may lead to seizures, cardiac and respiratory arrest and eventually death.
Cyanide poisoning is an example of histotoxic hypoxia resulting from tissue poisoning by $\rm CN^-$ ions. Unlike other forms of hypoxia where the concentration of oxygen is less in tissues, in cyanide poisoning, the concentration of oxygen is perfectly normal in both the extra- and intracellular fluid. It is the cell that is unable to utilize the oxygen present in/around it. As a result the arterial blood doesn't lose much oxygen during its course to the tissue as the oxygen gradient is not quite steep, resulting in an increase in the $\rm HbO_2$ concentration in the venous blood as well. Thus your skin gets cherry red, not blue like in the case when you are deprived of breathing oxygen, which occurs due to an increase in the concentration of deoxygenated hemoglobin in the blood.
Here is what happens at the molecular level.
The $\rm CN^-$ ions diffuse into the mitochondria. They have high affinity to the ferrous ion of the mitochondrial enzyme cytochrome c oxidase involved in the electron transport chain (ETC), one of the phases of cellular respiration where $\rm ATP$ is generated from $\rm NADH$ and $\rm FADH_2$. And it is this process that actually requires oxygen. The inhibited cytochrome c oxidase is of no good in transporting electrons, thus no $\rm ATP$ molecules are generated. The oxygen molecules waiting for those electrons remain empty handed resulting in the increase in the concentration of molecular oxygen. Remember, ETC occurs in almost all living cells except a few like RBC which get their major share of ATP from the highly inefficient anaerobic glycolysis. Also, $\rm ATP$ is the energy currency of our body and is required in a wide variety of bodily processes like osmotic balance, nerve impulse transmission, muscle contraction etc. With no $\rm ATP$ your heart and respiratory muscles can't contract, your medulla can't regulate breathing, your kidneys can't concentrate urine and the list goes on. Death is imminent if a high concentration of cyanide gets into your blood. The symptoms of panic like tachypnea and tachycardia (that result due to low oxygen in blood) are not usually seen unless the victim himself knows he is poisoned. The end effects like cardiac and respiratory arrest, seizures and coma, however, are similar to those of suffocation.
For further read: The Mechanism of Cyanide Intoxication and its Antagonism
I'm not a doctor, so I'm not 100% sure about the physiological differences, but on a molecular level there is one:
Cyanide blocks the complex IV of the oxidative phosphorlytaion, which will directly stop cells from consuming oxygen and producing energy needed to survive. This is mechanistically different from suffocation, where there is not enough oxygen in your blood stream to sufficiently power oxidative phosphorlytaion to produce energy (meaning complex IV could work, if it just had more oxygen).
During suffocation - or low blood oxygen - the body can react to the lowered oxygen supply (by increased breathing):
In humans, hypoxia is detected by the peripheral chemoreceptors in the carotid body and aortic body, with the carotid body chemoreceptors being the major mediators of reflex responses to hypoxia. This response does not control ventilation rate at normal pO$_2$, but below normal the activity of neurons innervating these receptors increases dramatically, so much so to override the signals from central chemoreceptors in the hypothalamus, increasing pO$_2$ despite a falling pCO$_2$
The mechanism for these oxygen sensors doesn't seem to be known, so we can't be sure if cyanide would also trigger them, but I think it's rather unlikely. I would also guess that the reflex reaction to low blood oxygen (triggered by these sensors) can additionally induce panic, which would likely not happen in cyanide poisoning. Other symptoms like dizziness, which are a more direct effect of neurons shutting down (or having not enough energy) should be similar.
Edit: The time it takes you to die is likely to be different as well. Cyanide acts fast - once it is in the cells - but depending on how you 'take' it, it could be similar to suffocation (although, you still might not directly notice the effects).