I think the NT cable won't fit in the NST charging point - the NC and I'm pretty sure the NT have a high current charger and a nonstandard USB fitting on the cable as it has extra pins and does not seat in other devices.
But you can use the NST cable to trickle charge the NT or NC from a USB port or the NST charger, or to sync to a computer. I have the NC charger in one room and the NST charger nearer the computer, and charge the NC with whichever cable is closest to hand unless it's gotten very low, in which case I fit it to the dedicated charger.
One word of caution on the charging: be sure you connect the cable first to your Nook Tablet, then to the charger. The high current can fitting can spark and damage the NT if you connect the device to a cable that is already live.