Cutwork
Fabric made "lacy" by cutting away
and binding edges with satin or buttonhole stitches.
This is not "real lace" but is shown here for comparison purposes.
It is not needlelace but rather cutwork embroidery, sometime called embroidered lace.

other names and varriations:
Richelieu, Broderie AnglaiseHedebo, Moorish Cutwork,
Colbert Embroidery, Renaissance Cutwork,
Spanish CutworkRoman Cutwork, Italian Cutwork  Venetian Cutwork,

 

Spanish Cutwork, (characterized by it's turned back hemmed satin stich edges)

Venetian Cutwork
Thickly padded buttonhole stitches (to resemble Point de Venise needlelace) The interior areas are frequently covered in fancy stitches to more closely resemble the lace. 
Roman Cutwork - the designs are so carefully done that a linited number of bars are needed to hold the design together. 
Italian Cutwork
Uses triple bars 
instead of single row of buttonholes
Colbert Embroidery, (most elaborate, heavily embroidered contrasting with very fine brides)
Richelieu, distintive buttonhole bars cross through the cutout areas (Richelieu bars) One source states that Richelieu haas picots on the bars, as opposed to Rennisance which does not.
Moorish Cutwork, colorful filings of silk and gold with gold embroidered cords forming loops. These loops are around the edges and connect the cuwork. The give the look of chains when they intersect.
Broderie Anglaise, (composed mostly of eylets of various sizes and shapes)

Hedebo, Danish cutwork which includes fillings of wheels, triangles and ladders. Uses satin stitches.
how to do Hedebo
Renaissance Cutwork, motifs are filled with buttonhole stitches.  Similar to Richelieu but without the picot on the bars.
Maderia Work
Another form of Broderie Anglaise that use eylets exclusively. It was made in the Island of Maderia (a Portugese territory) 
sources:
The Complete Book of Needlework by Therese de Dillmont
Cutwork, Hedebo & Broderie Anglaise edited by J&K Kliot
 

Cutwork Embroidery