What is the difference between generative and structural recursion?

Structural recursion happens when the "sub-problems" match up exactly with the possible pieces of the data.

For example, processing a list lox. The trivial case is when lox is empty. Otherwise the first sub-problem is dealing with the (first lox), and the second sub-problem is dealing with the (rest lox). You solve each sub-problem by calling a helper function, and you combine the solutions.

(define (process-list-of-x lox)
  (cond
    ;; trivial case
    [(empty? lox) ...]
    [(cons? lox)
     ; combine the solutions
     (...
      ; solve the first sub-problem
      (process-x (first lox))         ; data-def tells you what the first sub-problem is
      ...
      ; solve the second sub-problem
      (process-list-of-x (rest lox))  ; data-def tells you what the second sub-problem is
      ...)]))

What's different is that structural recursion tells you what the sub-problems are, where in generative recursion the sub-problems could be anything. You often need a new idea for how to break it up. A Eureka moment specific to the problem, not the data.

(define (solve-problem prob)
  (cond
    ;; trivial case
    [(trival-problem? prob) (... prob ...)]
    [else
     ; combine the solutions
     (...
      ; solve the first sub-problem
      (solve-problem (generate-first-sub-problem prob))   ; you have to figure this out
      ...
      ; solve the second sub-problem
      (solve-problem (generate-second-sub-problem prob))  ; data-def doesn't tell you how
      ...)]))

Also, structural recursion guarantees that it terminates because the sub-problems come from breaking up the data. In generative recursion the sub-problems can be more complicated, so you need some other way of figuring out whether it terminates.