As for the so-called Wrecking Crew, what Greg T has posted above is accurate. Another example is regarding Bob B. Soxx & The Blue Jeans. There were only three singles credited to that group, and all hit the Billboard pop charts, but on the flip side of each of those recordings, there was no singing; rather, there were instrumentals credited to Bob B. Soxx & The Blue Jeans that were actually performed by studio musicians (primarily members of the Wrecking Crew).
As for The Crystals, on two of the big hits credited to them -- "He's A Rebel" and "He's Sure The Boy I Love" -- Darlene Love & The Blossoms actually performed those songs. And Spector also utilized The Wrecking Crew on Philles label recordings credited to Ali Hassan (Al Kazan) and Steve Douglas & His Merry Men. [Douglas was a regular sax-playing member of The Wrecking Crew.]