While sex is your biological make-up (female, intersex, male), gender refers to the social meanings and consequences of that in a particular society and time. Gender is somewhat fluid, changeable and different in various societies and times. So, in some African countries women are expected to carry ceramic vases with water for miles. By contrast, in many western countries women are seen as fysiologically weaker and completely justified in asking their husband or boyfriend to put the carbage bin outside.
Divergent gender expressions and identities require character
There are traditional gender roles and gender expressions in a specific society and it requires character to go against them in your gender expression. But hey, Madonna, Lady Gaga and Prince have given us wonderful examples.
Gender identity is the meaning you yourself attribute to you biological sex. The current movies and documentaties about transgenders clearly show that you may be biologically a man, but feel yourself a woman. They also show that for some transgenders it is easier or more pleasant to alter their biological sex at some point.To be clear here, that requires character too! It is for them often too much of a hastle, if society keeps treating you (imposing traditional gender expectations) on the basis of what you biologically look like. Apparantly, society hates confusion.
Conchita Wurst, Winner of European Songfestival 2014
In the short run
While the meaning of gender is changeable, it is not so in the short run. So a girl and her boyfriend may have decided to have a child and to share all tasks. Then suddenly, after the child has been born everyone acts as if it is her job only to look after the child or to arrange child-care. Or the young man may be confronted with colleagues, friends and family warning him that he must think about his career.
Gender is a spectrum, but it requires hard work to go against the current traditional gender expressions. It is also takes courage to find, define and express your own gender identity, every period of your life anew. Respect!