The big difference in a lace frontal and a closure is the construction, the materials used, and how they are applied.
In GENERAL a lace frontal closure is meant to be bonded in place, as well as by attaching with the use of clips. The most popular method for installing a lace frontal closure involves sewing down the back of the frontal and using a bonding agent to glue the front hairline down. A lace frontal piece has a realistic hairline which is meant to mimic hair growing from the scalp.
Lace frontals cover a larger area than closure as they will have a temple to temple hairline. This larger temple to temple area in combination with the replication of a natural hairline allows for many off the face type of hairstyles that are not possible with a regular closure. Just like its full sized lace front wig counterparts, a frontal will require the sealing of the knots to help keep the hair secured firmly in the cap.
In GENERAL a closure piece is usually used for sew in installs/applications. If placed properly just behind the hairline, it can allow the wearer to wear a full weave with no hair left out while giving the appearance of a natural scalp area.
Closures do not run temple to temple. Instead they are placed in the horseshoe area at the top of a weave to close off the style. (Hence the name closure)
The most popular breathable closures are constructed from silk mesh with a poly strip or thin skin around the outer perimeter of the mesh which strengthens the mesh (for a sewn-in application) or to make bonding the closure easier. These closures allow for freestyle parting along the cap area. The addition of a flesh colored stocking under will help to add the look of a natural scalp to this style of closures. This type of closure may require the sealing of the knots (as in a lace frontal) to help keep the hair secured firmly in the base.