Attempt at understanding the Y combinator

gistfile1.scm

; http://www.dreamsongs.com/Files/WhyOfY.pdf

(define Y (lambda (f)
           (let ((g (lambda (h)
                     (lambda (x) ((f (h h)) x)))))
            (g g))))

; I understand it up to here.

; But then we have this:
; http://en.wikipedia.org/wiki/Fixed-point_combinator#Y_combinator

(define Y
  (lambda (f)
    ((lambda (x) (f (lambda (v) ((x x) v))))
     (lambda (x) (f (lambda (v) ((x x) v)))))))

; I haven't yet convinced myself these two are the same thing. Given the
; explanation in The Why of Y, I'd expect it to look like this instead:

(define Y
  (lambda (f)
    ((lambda (x) (lambda (v) ((f (x x)) v)))
     (lambda (x) (lambda (v) ((f (x x)) v))))))

; But maybe these are the same thing? It's hard to see how.

; EDIT: I've run a couple of rudimentary tests and they appear to both function
; correctly. So it turns out they probably mean the same thing, but I'm still not
; convinced. How can both be valid?