When metals like Zn and Cu react with concentrated nitric acid, nitrogen oxides are produced as by-products. The nature of the oxide depends on the metal's reactivity.
Zinc (Zn), being more reactive, reacts with concentrated HNO$_3$ to form nitrogen dioxide (NO$_2$), a brown toxic gas. Copper (Cu), though less reactive, also forms NO$_2$ with concentrated nitric acid. In both cases, NO$_2$ is the nitrogen oxide formed due to the strong oxidizing nature of concentrated HNO$_3$.
Thus, in both reactions, the nitrogen oxide evolved is NO$_2$.