Why are different colours observed in octahedral and tetrahedral complexes for the same metal and same ligands?
Extent of splitting of $d$-orbitals is different in octahedral and tetrahedral field. CFSE in octahedral and tetra federal field are closely related as.
$$\Delta_t=\left(\frac{4}{9}\right) \Delta_o$$
where, $\quad \Delta_t=$ crystal field splitting energy in tetrahedral field
$\Delta_0=$ crystal field splitting energy in octahedral field
Wavelength of light and CFSE are related to each other by formula
$$\begin{aligned} \Delta_0=E & =\frac{h c}{\lambda} \\ E & \propto \frac{1}{\lambda} \end{aligned}$$
So, higher wavelength of light is absorbed in octahedral complexes than tetrahedral complexes for same metal and ligands. Thus, different colours are observed.