What is the difference between rectus plication and abdominoplasty and Tummy tuck?

Thanks for your question. Abdominoplasty and tummy tuck are the technical and colloquial names for the same procedure:  the removal of stretched lower abdominal skin and the tightening of stretch abdominal muscle/fascia which has usually occurred after pregnancy or significant weight gain and loss.  Rectus plication refers to the abdominal muscle/fascia tightening component of the procedure. It's not really the muscles that are stretched, but, rather, the fascia which is the lining stretch layer of the abdominal wall that covers the abdominal muscles. Not performing the plication will almost always compromise the quality of the cosmetic result. 

Rectus plication is tightening up the adomenal muscle. A tummy tuck most of the time includes that. A tummy tuck removes the excess skin and fat from the abdomin.