Nothing strange about suffering from SAD and feeling "extroverted" when you're around people you're comfortable with. In fact, this is a classic scenario.
When you're with strangers all sorts of associations come up, like a flood of hormones that make you suffer from the panic attacks, worry about coming off like an idiot etc. When you're comfortable at home, all sorts of associations come up like a flood of hormones, and you start chattering away maybe even unconsciously making up for your SAD by being TOO talkative at home :
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This makes me believe that there are different types of SAD, and this particular type that you, and many people here have is more an automatic behavioral response that can be reprogrammed using all the various bits of wisdom that you could find in the previous posts here.
Introversion is about where you get your energy. A lot of entertainers including comedians and actors would consider themselves introverted even if they can work a crowded room like putty in their hands. They just need that time alone to collect themselves again.
If they do a study I honestly won't be surprised if they find out that more entertainers are introverted than extroverted. Entertainers are usually insightful about human nature (especially the master actors and comedians) and that takes a level of observation and introspection that might bore extroverted people. So , yes there is a difference between being shy and being introverted.