Their building blocks may be different, but if your Turing complete language does not include a for loop, you can write code that will simulate a for loop. It may not be efficient, and it may not be core, but you can do it.

If you can implement a system which analyzes one such language, you can inefficiently port it to other languages by simulating those other languages in your first language.
This may, however, fall afoul of your "useful" clause in terms of practicality regarding CPU and memory use.

Equivalent to looping, I buy that. But equivalent_to_X ne X.

The difference is in terminology and syntax (and efficiency of implementation), but those do not change the essential nature of looping.
It is more of an: ("X" ne "X/2 + X^0 + 0.5 * X - 1") and (X == (X/2 + X^0 + 0.5 * X - 1))
Where the LHS is Looping, and the RHS is equivalent to looping in a language without core loop support.