Tried to figure this out from previous posts but am still confused, and afraid.

Our 30 year old exhaust fan had a light, fan and heater. We're replacing it with a fan/light combo, no heater.

The switches independently operated the light, fan and heater. I had an electrician remove the heater switch and turn the 3 gang switch into a 2 gang. 

I removed the old fan/light and there were only 2 supply Romex cables- the light was supplied by a Romex with a hot black wire, normal.

The fan wire has a hot white wire. Why is that? 

Do I just connect the white wire to the black wire of the fan motor?![enter image description here] These photos show the 2 romex cables- one is switched to the light, and one is switched to the fan. The one to the fan shows a voltage tester on the white wire. The new light /fan wiring is shown. Does the black wire in the Romex go to blue, and the white wire of the Romex go to black of the fan?(https://i.sstatic.net/2Mq3Q.jpg)![enter image description here](https://i.sstatic.net/Cp7SS.jpg)![enter image description here](https://i.sstatic.net/Hk3gK.jpg)![enter image description here](https://i.sstatic.net/EjXSd.jpg)