Shy Introvert vs. Shy Extrovert

Let's get the basic difference out of the way: Extroverts need interaction with an energy source outside of themselves, usually in the form of socializing. Introverts spend energy when interacting with others will need a break, some sooner than others. This doesn't inherently make either group shy or not. It just means that two different ways of getting energy. It does not mean that an extrovert is necessarily a people person or that an introvert has no desire to be with people.

Now let's talk about the two different types of shy people, starting with the extroverts. I'm an extrovert, and there were periods in my life when I had some social anxiety, because I know that I was very weird and that I tended to talk too much. I was afraid that people might feel uncomfortable with my energy levels, and other such things that could go wrong. It's not that I didn't enjoy being around people, since they energized me. It's that I had low self-esteem and not a lot of social skills to begin with. This is especially true is an extrovert has Asperger's Syndrome, since they're neurologically handicapped when it comes to reading social queues, and it takes a lot of extra time to develop those skills. Many people with Asperger's Syndrome aren't shy and they plow ahead with their foot-in-mouth conversations, but others are more self-aware and don't want to put their handicap out on display, so because of all of that self-doubt they avoid contact with others, or getting too involved in group conversations. This is incredibly draining for them, and can lead to depression.

I would also say that it's possible for an extrovert to not be shy, but nonetheless be anti-social. The prime example that comes to my mind is Dean Winchester, an obvious extrovert who doesn't want a lot of people in his life. It's obvious that he's an extrovert, because he'll hang out with other people when he has to wind down, but due to his line of business, he's a bit hostile to most folk, and finds some rather extroverted ways of warding them off. I can also think of some ENTJs who get energy from the pursuit of something, and not from aimless social interaction. That is to say, they don't have time for meaningless relationships and only care about working with people with whom they can get things done. So there are many different types of introversion.

As for introverts, I think that this is much more intuitively obvious to grasp. They're often shy for the same reasons: they don't feel adequate enough to deserve socializing with others. It's simple social anxiety. Except you add on top of it that they have to spend energy to interact with other people, and it compounds the problem. The good news is that when they're alone, they do get a lot of energy. It's just that they don't have an easy time finding ways to channel that energy.