Sneakers got their name from the rubber sole — quiet enough that you could sneak up on someone. The word appears in American print as early as 1887, referring to shoes with India rubber soles that made no sound on hard floors. Kicks came later, from the street, from basketball courts and city blocks where the shoe on your foot said something specific about who you were and where you stood.
The two words mean the same thing. They come from different places. Sneakers is the catalog term, the retail term, the term your parents used. Kicks is the culture term — the word that came from the people who actually cared most about the shoe, who camped outside stores and kept boxes stacked in closets and knew the difference between the '85 colorway and every reissue since. Sneakers is the object. Kicks is the obsession.
The trajectory of the sneaker — from athletic equipment to cultural artifact to investment-grade collectible — is one of the stranger business stories of the last fifty years. A rubber-soled shoe designed for a basketball court is now traded on stock exchanges and stored in climate-controlled vaults. The shoe did not change. The culture around it did.