What kind of memory does the device memory of modern smartphones belong to?
All of the above in some form or other.

The RAM listed on the specifications will be DRAM of some sort. Very similar to the RAM in a desktop PC only optimized for low power rather than raw speed. 

There will also be some SRAM in the form of the CPU L1 and L2 cache, since that is determined by the CPU used rather than something the phone manufacturer can change it's not normally listed on the specs. 

And then there will be NAND FLASH providing the main storage, this is like an SSD hard drive in the PC.