I'd like to check a definition:

If $X$ is a scheme, what does it mean to say that $X$ is "defined over $\textrm{Spec }\mathbb{Z}$"? Is this a precise statement? Certainly this statement requires that $X$ is finite type over $\textrm{Spec }\mathbb{Z}$.

If $X$ is a projective or affine variety over $\textrm{Spec }\mathbb{C}$ (with choice of embedding) we can ask if the coefficients of the equations defining it are integers, and maybe call such a scheme to defined over $\textrm{Spec }\mathbb{Z}$. Other than not being "coordinate free", it is also easy to get schemes that are better said to be "defined over $\textrm{Spec }\mathbb{Z}[1/N]$" (in particular, there are lots of examples when a construction is defined over the latter scheme, and a goal is to make it defined over $\textrm{Spec }\mathbb{Z}$).

$\textbf{Question:}$ If $X$ is a scheme, does the phrase "defined over $\textrm{Spec }\mathbb{Z}$" mean that the structure map to $\textrm{Spec }\mathbb{Z}$ is fppf? (or is the base change to say $\textrm{Spec }\mathbb{Q}$ of a scheme with such a structure map).