In suffocation or asphyxiation you are actually deprived of breathing oxygen. 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 respiratory rate, force of contraction and relaxation of respiratory muscles and heartbeat rate. Simply put, you get panicked. Prolonged suffocation may lead to seizures, cardiac and respiratory arrest and death.
Cyanide poisoning is an example of histotoxic hypoxia resulting from tissue poisoning by $\rm CN^-$. Unlike other forms of hypoxia, where the concentration of oxygen is less in tissues, in cyanide poisoning, the concentration of oxygen is actually perfectly normal in ECF and ICF. It is the cell which is unable to utilize the oxygen present in it. As a result the arterial blood doesn't lose much oxygen to the tissue as they themselves have adequate oxygen, resulting in an increase in $\rm HbO_2$ concentration in blood.
Thus your skin gets cherry red, not blue like when you get deprived of breathing oxygen which happens due to an increase in concentration of deoxygenated hemoglobin in 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, one of the phases of cellular respiration where $\rm ATP$ is generated from $\rm NADH$ and $\rm FADH_2$. And it is this process which actually requires oxygen. The inhibited cytochrome c oxidase is no good, thus no $\rm ATP$ molecules are generated from ETS. And, the oxygen molecules waiting for those electrons remain empty handed explaining the increase in molecular oxygen concentration. Remember, ETS occurs in almost all living cells except few like RBC which get their major share of ATP from the highly inefficient anaerobic glycolysis. Note, $\rm ATP$ 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 muscles and respiratory muscles can't contract, your medulla can't regulate breathing. You will go into cardiac and respiratory arrest. It may result into seizures and coma. Death is iminent if a high concentration of cyanide gets into your blood.
The symptoms of panic are not usually seen unless the victim himself knows he is poisoned . Well, that is due to your fight/flight response. The effects like cardiac and respiratory arrest, seizures and coma are similar to those of suffocation because it is due to low $\rm ATP$ production in both cases.