Lace is created during the making of the fabric. Embroidery is stitching placed on top of finished fabric.
Genuine lace is a fabric or trim solely created by twisting or knitting many individual threads into an airy pattern. Unfortunately some companies in the lingerie business are referencing embroidery on the garment with a similar design to lace as actual lace, but it is not truly.
Both lace & embroidery add to the cost of the garment.
Some lace is handmade and some made on machines. Handmade lace is obviously more labor intensive, both methods have complex patterns that must be carefully designed, programmed, and implemented. Lace manufacturing is labor intensive which adds to cost.
Learn more about lace.
Learn more about embroidery.