There are several variants for P8:
GRA-UL00 - LTE/WCDMA for China Unicom ("open"), dual SIM;
GRA-TL00 - TD-LTE/TD-SCDMA for China Mobile, dual SIM;
GRA-CL00 - LTE/CDMA for China Telecom, dual SIM;
(the 3 above comes with GRA-*L10 sub-variants with 64GB storage instead of 16GB)
...and finally GRA-L09 - international LTE with European bands, single SIM.
The dual SIM variants have one slot for either a nano-SIM or a MicroSD card, and a dedicated slot for a nano-SIM, as shown below. You did mention that one SD and one nano-SIM can be inserted at the same time - that means you do own a dual SIM variant, just didn't get the correct way to utilize it.