In Photoshop you are working on bitmaps while in Illustrator you are working on vectors. It'a a big diference. When you are pasting your work done in PS into Illustrator you place a bitmap - a rectangle (unless you are working with paths). If you wan't the image to have a diferent form you should draw a vector shape and mask the image with this shape, like shown here: http://rubberspark.com/clipping-mask-in-adobe-illustrator/

In Photoshop you are working on bitmaps while in Illustrator you are working on vectors. It'a a big difference.

When you are pasting your work done in PS into Illustrator you place a bitmap - a rectangle (unless you are working with paths). If you want the image to have a different form you should draw a vector shape and mask the image with this shape, like shown here