Spandex, the name commonly used in the U.S and “Elastane” in the rest of the world, is a synthetic fabric that is prized for its elasticity. Contrary to popular belief, the term "spandex" is not a brand name, and this term is used to generally refer to polyether-polyurea copolymer fabrics that have been made with a variety of production processes.
Elastane is commonly used in form-fitting consumer apparel. In most cases, pure elastane isn't used in garments, and instead, small quantities of this fabric are woven into other synthetic, semi-synthetic, or organic fibres.
Lycra is simply a trademarked brand name for this synthetic fibre.
Spandex and elastane are interchangeable terms that mean the same thing.