Categories of time series

I am trying to classify different kinds of time series, but find myself missing good vocabulary. I don't mean that, for a given time series, I try to classify its datapoints into clusters or the like. Instead, I am looking for categories into which I can sort different time series. Two time series belonging to the same category should be apt for similar time series analysis.

For instance, in some processes measured you find that essentially only two values are assumed, the lower is often zero. I like to call this kind of time series on-off-time series in my head.

Another category would be continuous, periodic time series like the measured temperature.

Is there an official name for these categories? Does the theory of classifying time series have a more distinguishable (than classifying time series) name which I don't know yet?