Re: NM to pool filter
If you look at 680.21(A)(1) It tell us
The branch circuits for pool-associated motors shall be installed in rigid metal conduit, intermediate metal conduit, rigid nonmetallic conduit, or Type MC cable listed for the location.
So the first requirement is a motor that is for a pool must use one of these wiring methods.
Now 680.21(A)(4) allows any wiring that is inside of the house to use any of the wiring methods recognized in Chapter 3. Including NM
But if you look at 680.21(A)(5) If the pump motor is A listed cord-and-plug-connected pool pump incorporating an approved system of double insulation, It can use any of the wiring methods recognized in Chapter 3
So from what I get is that once you hit the outside wall of a house and the pump is not double insulated and cord and plug connected you must use a metal conduit or ridged non-metal conduit. There's not anything that say's anything about whether or not the circuit also supply's a heater unit for the pool but there might be a chapter 3 article that might have something to say about using the same circuit for both if the load is over 50% of the circuit. And if a feeder is used to supply a panel then these feeders have to be installed in conduit even if it is inside. 680.25 and 680.25(A)
Somthing else to remember is you have to run a grounding conductor in the conduit and it has to be insulated. 680.21(A)(1) and 680.21(A)(4)