Is a CEK machine an implementation of a CESK machine?
The store in a CESK machine is the "heap", where mutable pointer-based data structures live. 


If your language is purely functional, then its operational  semantics don't need a store. Take it out, and you get the CEK machine.
If your language does not have control operators (such as call/cc or exceptions), then you can get away with the K (the continuation). 
If you don't want to model environments and closures explicitly -- that is, you don't mind a substitution-based semantics -- then you don't need the E (the environment). Calculi for classical logic (which have control operators but no state) often end up looking like CK machines.
If you have a purely functional language without control effects, then you can use the program itself as the abstract machine state, and the reduction rules will be the small-step operational semantics for that language.