Inserted lace is lace inserted between ‘spaces’ or openings in fabric. At the edge of one fabric, lace begins; where the lace ends, solid fabric resumes. Inserted lace replaces the fabric so no fabric is behind the lace.
Applied lace is rather like applique — lace is sewn on top of the fabric. Often the lace is the same color; other times, it is a contrasting shade.
Sandwiched lace is lace that is in between two layers of fabric or sandwiched. Usually the top fabric is sheer to show off the pretty lace underneath it. The bottom fabric may be of the same shade, or a contrasting color.
See this previous post for information on illusion lace.