Nope, DDR4-4000 is not "running at 4 GHz". SDRAM 133 ran at 133 MHz, but DDR numbers have always multiplied their frequency by "number of simultaneous transfers" or something like that. (The first DDR multiplied by two - "double data rate".)
DDR3-2133 has a 266.67 MHz memory clock, and a 1066.67 MHz bus clock (x 4), and a "data rate" of 2133 "mega-transfers per second". And a bunch of other details, it's complicated.
The point is, don't take the "4000" literally. It's complicated. And timings and latency can differ between models of the same "data rate".
Wikipedia has a good table for DDR3: https://en.wikipedia.org/wiki/DDR3_SDRAM#JEDEC_standard_modu...
DDR3-2133 has a 266.67 MHz memory clock, and a 1066.67 MHz bus clock (x 4), and a "data rate" of 2133 "mega-transfers per second". And a bunch of other details, it's complicated.
The point is, don't take the "4000" literally. It's complicated. And timings and latency can differ between models of the same "data rate".