They are patients. In a few settings, such as outpatient mental health, patient do prefer to be called clients, but for the most part patients find the term offensive if they have a view either way.
This came from an ANA recommendation from one of their committees, they admit it wasn't very well thought out and they reversed their position then next time this committee was convened, but by then the damage was done, every Nursing school in the country had already latched onto it as the next big thing.
There have been survey's on the topic, and not surprisingly, patients don't like the term because it implies that they are a participant in a financial or business relationship, rather than a participant in a therapeutic relationship which is what the term "patient" implies.
As it turns out, patients like to feel like they are seen as someone needing care, rather than a billable source of cash.