Shown here is Catasetum saccatum . Cattleya species and hybrids are the big frilly orchids popular in corsages. Some have one leaf per stem, some have two or three. They like lots of light. This is Cattleya skinneri .
Cymbidium is a genus of terrestrial orchids.
Their long leaves give them higher space requirements than most other orchids. The plant shown here is a miniature Cymbidium hybrid . Dendrobium generally has canelike stems, though some form clusters of small pseudobulbs that hug the ground. They like small pots and good air circulation. They're fairly common at nonspecialist nurseries and other places orchids are sold.