1333MHz ram runs only 666MHz

Most reporting apps report the unmultiplied clock 

As you can see it lists the unmultiplied clock in brackets. If your RAM is showing say 333 in brackets (in the case of your DDR3 1333) then you know it is working at half it's rated speed. If it shows 666 as you stated in your first post then it is working as it should. This is the reason for the DDR adage at the front of the RAM type, DDR = Double Data Rate and the number after that denotes generation so DDR, DDR2, DDR3 and DDR4 with each successive generation improving performance. So in theory DDR @400 (200mhz x2) should be slower than DDR2 @400 which will be slower than DDR3 clocked  @400 etc

I hope this clarifies things for you. The DRAM frequency is always listed as the unmultiplied figure. CPUz is the go to tool to check this but even in speccy it lists RAM as "Dual/Single Channel (model) @666mhz". Note that it has "mhz" on the end, this usually means that it is listing the DRAM frequency not the rated speed.