Bobbin lace comes by several different names such as pill or pillow lace, cushion lace, thread lace and bone lace. Sometimes it is referred to as Lyme and Honiton lace as well.
Here is a nice story, although I have no idea if it is true, entitled "How Cushion Lace Was Invented". This story was published in Godey's Magazine 1861.
Uses of lace were described in detail in Household Words Vol 2. Some examples are:
Mechlin lace "is used chiefly for trimming night-dresses, pillow-cases, coverlets &c."
Valenciennes lace "is employed for ordinary wear"
Brussels lace "is reserved for bridal and ball-dresses"