It seems that there are similar symptoms shown by people who suffer social anxiety and shyness, but what is actually the main difference between them? Thank you.
It's a matter of degree.
First of all, "shyness" is not a psychological or psychiatric term, but an everyday English word denoting a commonly observable personality characteristic on a par with courage, cheerfulness, or honesty. The meaning of "shyness" is not exactly defined, and people may use the word "shyness" to refer to different kinds of behaviors, from being introverted (and not interested in social interaction) to being afraid of social interaction.
"Social anxiety disorder", on the other hand, is a psychiatric and clinical psychological term, the meaning of which is clearly and exactly defined by the scientific community. That means that while there is of course some debate about what social anxiety disorder is, there is agreement about what the term currently means.
As for the relation between shyness and social anxiety disorder, shyness is generally conceived as a mild from of social anxiety, which leaves the person able and functioning in his or her life, while social anxiety disorder is such a strong anxiety that the person suffering from it cannot partake in a normal way, is disabled by this anxiety, and suffers from its effect.
The accepted answer is correct, it is basically a matter of degree, plus some other things.
Adding more details, refer to the following definition of Social Anxiety Disorder (previously known as Social Phobia) taken from The Diagnostic and Statistical Manual of Mental Disorders 5th edition:
Perhaps more specifically, it is written in this DSM-5 Social Anxiety Disorder Fact Sheet, that (emphasizes are from me):
It's also important to note that there's been a great deal of effort in defining abnormality (disorder). I don't own any version of DSM (I do have a physical copy of Clinical Psychology by Andrew M. Pomerantz and Abnormal Psychology by Nolen-Hoeksema, but they are currently borrowed by friends), but the criteria for abnormality usually involves (as seen here and here):
And it usually has to last for a certain period of time before it can be diagnosed as a disorder.
DO NOTE, however, that no matter how much you feel that you or anyone you know seems to fit with one or more of the above criteria, you CAN'T simply conclude that he/she/they have a mental disorder. Diagnosis of mental disorder should only be done by someone who is certified by law to do so, such as psychologist or psychiatrist. And even then, it should be done only after complete, thorough, and proven analysis.