Definitions I have heard range from any wetland supported by groundwater to suggesting specific plant species and groundwater chemistry parameters. Some consider it rare habitat, which may prompt severe mitigation requirements for impact. I once had a hydrogeologist tell me there are only 2 types of wetlands, fens and bogs, its either dominantly groundwater input, or it isn't. From a functional perspective I do not believe fens have to have organic soil, as many classic wetland definitions reqiuire.
Fens exhibit much greater species diversity than bogs.
This physical setting provides an environment for specific and often rare hydrophytic plants, including nearly a dozen species on the state endangered species list. However, I have heard various scientists use the term fen to also describe slope wetlands whether the groundwater source was alkaline or not. Plants that are fen habitat specific are rare because the habitat is rare. In Minnesota fens are rare because they historically occurred in the area of the state where most of the land was converted to agriculture and thus were one of the most impacted wetland types in the state. I never have looked into any information regarding fens in other states and therefore am unable to say if the Minnesota definition is similar to what other states may have on their landscapes.