Translation:Men and women are people of different genders.
"People" is the default way to say a group of human beings. If you want to emphasize their individuality, sometimes persons will be used for precision. (For example, in legal language, where you're referring to their individual choices and liability, not their action as a group, you'll often see a phrase like, "any person or persons, known or unknown"). I'm not sure if it's tied to the other use of "person," to mean someone's physical body: "Did the accused have the murder weapon on his person?"
So, "how many people are in your group" (waiter, trying to find you a table) and "there are a lot of people here" and "She's such a people person, she loves people, while I prefer the company of my dog"...but, "persons charged with a first offense for drunk driving are subject to the following penalties."