The reaction rate order reflects (unconditionally) the stoichiometric coefficients only for elementary reactions without more complex reaction mechanism. For complex reactions with a reaction mechanism schema, the order may or may not reflect the stoichiometric coefficients.
Imagine the reaction
$$\ce{3 A -> B}$$
has the reaction mechanism:
$$\ce{2 A -> C}$$ $$\ce{2 C -> B + A}$$
For a steady state:
$$\text{d}[\ce{C}]/\text{d}t = 0 = k_1[\ce{A}]^2 - k_2[C]^2$$ $$[\ce{C}] = \sqrt{\frac{k_1}{k_2}}[\ce{A}]$$
Then for the product $\ce{B}$:
$$\text{d}[\ce{B}]/\text{d}t = k_3[C]^2=\frac{k_3}{k_1k_2}[\ce{A}]^2$$
therefore $\ce{3 A -> B}$ has in the steady state the reaction kinetics of the 2nd orderthe second order.
If not in the steady state yet, the reaction rate equation would be more complicated.
Different case: the reaction $\ce{3 A -> B}$ is triggered by UV/Vis light absorption:
$$\ce{A + A ->[h \nu] C}$$ $$\ce{A + C ->[h \nu] B}$$
The reaction rate is in wide range of [A] controlled by the incident photon rate, independent on the [$\ce{A}$], so the reaction kinetics wrt $\ce{A}$ would be of the zeroth order.
If [$\ce{A}$] is too low, part of light can transmit through and it would become [A] dependent (but not with an integer order).
If [$\ce{A}$] is too high, the light could be absorbed in a surface layer and the reaction rate would be partially controlled by diffusion. It would become [A] dependent again (not with an integer order).