The correct answer to this open question is the following.
The examples of “gendered” interaction that I noticed regarding the ways in which women and men socialize regarding demeanor, uses of space, starting, touching, smiling, and language are the following.
Women use to strictly define a clear line that men should never cross. It is a matter of education and respect. Women like to have a decent and proper distance when relating to men. They like this distance when having conversations, like to smile and laugh.
When they are with other women, they don't mind getting closer or touching their hair. Women's feminine movements are something that makes them unique.
On the other hand, men like to be together. They greet each other with handshakes and hugs. They are tougher in their relationships. They do not take care of their appearances and looks, as women do. They speak to each other using stronger words or bad language. Women are more prudent in this sense.