The history of lace-making deserves an entire book on the subject.  The art of making it goes back in time further than even some fabric weaving. Knotting techniques actually trace back to basket making. As lace-making evolved into an art form, so did the demand for it. Like fabric has a weave, lace has different patterns. Here are a few of the most common:

Alencon-Floral patterns on mesh or net background outlined in cording. Has a three-dimensional look.
Juliet dress by Amy-Jo Tatum//source
Chantilly-Floral or foliage designs on a net background. Generally has a scalloped edge.
Juna dress by Amy-Jo Tatum //source

Cluny-Crocheted lace in heavy cotton also known as Irish lace. Chic in the swinging 1960s for mini wedding dresses and granny gowns.
Eyelet-Actually a woven cotton with eyelet cutouts and embroidery.
Peau d'Ange-Delicate version of Chantilly lace made with a flossier yarn.
Schiffli-Embroidered design on a mesh or organza background. Typically has a scalloped border.

Venice-Heavy lace with raised designs. Usually a single motif with an open background.