A person sighs through inhaling deeply through his nose while exhaling the carbon dioxide through his nose and mouth. The act of yawning looks like you are stretching your mouth and breathing in deeply. Yawning is generally associated with tiredness and boredom. Sighing could be for a myriad of reasons. It could be due to depression, fatigue, or an even better example of when people sigh is during a movie that touches you in some way.
People tend to sigh as a form of empathy or a loving feeling. We yawn to gather more oxygen inside our body system. However, too much yawning can be indicative of poor sleeping habits, insomnia, sleep apnea, and other health disorders.