Nerd and geek are not the same although, like me, you can be both.
Nerd: A nerd is into science, mathematics and technology. Your typical nerd has probably entered at least one science fair and may have even won. The nerd knows what all the weird buttons do on a calculator. Not only that they can still use a slide rule you know, in case the batteries run out. They love robots. They read real hardcore old school science fiction like
Heinlein, Asimov, Le Guin, and Clarke. Yourr nerd will sit in theaters while watching a science fiction film and constantly bitch that they got the physics all wrong. They will go absolutely ballistic if there is a loud explosion in the vacuum of space.
Geek: A geek is into fandoms. They are often cosplayers and they are really into comic books. Their natural habitat is Comic Con in San Diego. They are so into their fandoms that they know all of the various nuances of the “universe” of each. The Star Wars universe has a certain set of laws which are different from the Star Trek universe. They will debate “Kirk or Picard” and sometimes even come to blows with their tiny little geek hands. The men often have fringes of beards around their necks and will remind you of the “Comic Book Guy” from the Simpsons. Your male geek when given an opportunity to speak to a beautiful girl cosplaying Steampunk Harley Quinn he will critique the costume rather than admire the girl.