Happy birthday :-)
Here's a comparison between the two, Woodcock Johnson (WJ) and Weschler's "intelligence" test (WAIS) (from Woodcock Johnson). Notice right off the bat that WJ's looks at just "general intelligence" versus Wechsler's "full scale IQ" - I can see why your psychiatrist would feel the Wechsler more helpful/"complete":
http://www.riverpub.com/products/wjI.../pdf/asb-1.pdf
I don't know anything about a "Wyatt" -- Wechsler's tests are known as "WAIS"(Wechsler's intelligence test) and "WIAT" (Wechsler's Individual Achievement Test) so I imagine you're wanting all "Wechsler" versus WJ/Woodcock Johnson. So, your psychologist wants you to compare the WAIS to the WIAT, "Intelligence" to "Achievement" -- does that make more sense to you?
Good luck today!