That's still introversion. It doesn't mean you're incapable of such actions, it more means you only do it around those who you feel comfortable with or are close to.
Extroversion means you can be outward almost everywhere and with anyone.
This topic is very topical to me, as I'm in a pretty hostile work environment almost everyday with two borderline sociopathic extroverts.
They are almost incapable of emotions such as empathy or change. They actually thought I was just crazy until I had to literally explain to them what introversion even was.
Further proof these two never deal with anyone who's not exactly like them, which is sad in a business where interaction is the biggest part.
I do enjoy writing, but the reason for my length here on forums like this is that I love detailed conversations with people and really getting to know someone.
Introverts dominate the internet and its them I generally get along with more, due to our shared outlook and penchant for long discussions. That's generally who I befriend.
And, of course, they saw me one day reading one of the novel length emails between me and a new friend and couldn't have been more confused at how or why I'd want to discuss something in depth like that, especially since it was a girl.
To them, you wine and dine and then just screw a woman, it's so foreign to them to develop a tight intimate bond first.
I hope you never have to deal with morons like these two extroverts. It's not extroversion that's the issue, it's that mixed in with their other traits.
It's extroverts like that that make introverts either retreat further back or become extremely violent.