To move through the water is driven by rhythmic contractions of your entire body; takes water, which is introduced into its gastrovascular cavity and ejects it, using it as "propellant".
The concept of jellyfish is not taxonomically but morphological. Many cnidarians have an alternation of generations, with sessile polyps that reproduce asexually and pelagic jellyfish that carry out sexual reproduction. Only anthozoans lack a jellyfish form; the other three classes of cnidarians (hydrozoans, scyphozoa and cubozoans) have polyp form and jellyfish form; said jellyfish have distinctive characteristics in the three classes, so that we can speak of hydromedusae, squamomed jellyfish and cubomedusa respectively.