mmcp42:
If I understand it correctly...constant int TheValueOne=1;will take up memory
#define TheValueOne 1doesn't take up any space
so I guess it saves a byte or two
can't work out why "constant int" is "more modern" though?
That is not true, and depending on the compiler a define may take up more memory than a const. The thing is that the define sort of creates a copy (maybe several copies if you use it a lot) of the value, whereas the const int is a single object. Think about it, where is the 4 stored? It must be in the memory somewhere.
I'm no Arduino compiler expert, but it could be that #define is faster when it comes to execution.