Here's some stuff I found:
While each is predominately white; side-by-side comparison tells them apart. Wipers have a bold stripe pattern. White bass stripes are less pronounced. Wipers take on more of a sleek 'torpedo' shape. "The most obvious difference, though, is the tongue patch," says Mack. "On a white bass, there is a 'U' shaped patch on the top of the tongue. On a wiper, the patch resembles two small unconnected ovals."
I had looked up the difference between a wiper and white bass early this spring when I caught a baby wiper somewhere I didn't expect them to be.  There is a difference in the fins if I remember correctly and that is the only way to tell them apart when they are young (other than the quote I posted above).  One thing about that quote, it claims wipers are more torpedo shaped, maybe compared to white bass, but certainly not compared to striped bass.
Here's a link to a white bass/wiper comparison...
I wish I could find the info I had about the fin differences.