Demand Factor. The ratio of the maximum demand of a system, or part of a system, to the total connected load of a system or the part of the system under consideration.
Total connected load IMO is non continuous + 125% of continuous = demand factor = service/feeder calcs per Art 220
The total connected load is the sum of the branch circuit loads on a feeder/service. The demand load on a feeder/service is the sum of the branch circuit loads after any demand factors in Art 200 Part III, IV or V have been applied. 125% has nothing to do with "demand factor," it is only used in determining minimum conductor and OCPD
SIZE.
For example, if you had a feeder with 100A non-continuous load and 55A continuous load, then the load on the feeder is 155A (not 168.75A.)
Per the first sentence in 215.2(A)(1), you would need a feeder conductor with an Ampacity that is not less than 155A.
Per the second sentence in 215.2(A)(1), the minimum feeder conductor
SIZE would have to have an ampacity, before adjustment or correction, that is not less than 168.75A. This would be 2/0 AWG.
But consider if the feeder was run in a common raceway with another feeder such that there are 6 ccc's. A #2/0 THHN would have an adjusted ampacity of 195*0.8=156A. A 2/0 THHN with an ampacity of 156A would be large enough for the 155A load.
I never hear of anyone going through art 220 and coming up with a load figure then going back and trying to add to it for continuous loading of certain components.
The Annex Examples D3 and D3a do just that. They calculate the "load" first, then they calculate the minimum feeder and OCPD size by adding 25% to the continuous portion of the load.
There's no harm in calling the load 100% of noncontinuous plus 125% of continuous, it just may force you into a larger conductor size than needed. As in the example above, if you called the load 168.75A instead of 155A, then you cannot use the 2/0 with an adjusted ampacity of 156.