Following someone is a one way relationship. When you Follow someone it means you'll see items they share publicly, but your items won't show up for them. Think of it like following a celebrity on Twitter.
Friending someone on the Xbox One is like Friending on the Xbox 360. It is a two-way connection. You see their activity, they see yours.
In order to Friend someone you first have to Follow them. When they Follow you back, the two of you become Friends.