Articles from the aquaticcommunity.com and the Nature Conservancy suggest that freshwater jellyfish, Craspedacusta sowerbyi, are more closely related to the Genus Hydra. From the Nature Conservancy article:
It should be known that though Craspedacusta sowerbii is touted as a jellyfish, some argue it is more related to the family Hydra than a "true" jellyfish. Many researchers still call it as such, but others may simply refer Craspedacusta as a jelly. The main difference between Craspedacusta swerbii and "true" jellyfish is the presence of a velum. Its velum is a thin, circular membrane around the cap that helps propel, or move, the jelly forward.
An articles from the US Geological Survey (USGS) states that Craspedacusta sowerbyi is a hydrozoan that can take the form of a jellyfish. From the USGS:
Craspedacusta sowerbyi is a hydrozoan (Phylum Cnidaria, Class Hydrozoa), which is most easily identified when it takes the form of a small, bell-shaped jellyfish, known as a hydromedusa.
The Merriam-Webster dictionary defines a jellyfish as follows:
a free-swimming marine coelenterate that is the sexually reproducing form of a hydrozoan or scyphozoan and has a nearly transparent saucer-shaped body and extensible marginal tentacles studded with stinging cells
This definition, to me, seems to suggest that Craspedacusta sowerbyi is a jellyfish, however there must be some other reasoning that I'm missing that makes others believe that they aren't. Any clarification would be greatly appreciated.