Let q be an even power of a prime p, and let \(\mathbb {F}_q\) be the finite field with q elements. For \(A=(a_{ij}) \in GL(3, \mathbb {F}_q)\) , \(C_A\) denotes the plane curve defined by the equation \((x^{\sqrt{q}}, y^{\sqrt{q}}, z^{\sqrt{q}}) A \, (x,y,z)^t =0.\) We call \(C_A\) a Hermitian-relative curve. Let \(A^{*}=(a_{ji}^{\sqrt{q}})\) be the conjugate transpose. Then \(C_A\) is a Hermitian curve if \(A=A^{*}\) , which is an important curve for various reasons. Two Hermitian-relative curves \(C_A\) and \(C_B\) are projectively equivalent if and only if there exists \(T \in GL(3, \mathbb {F}_q)\) such that \(B=T^* A T\) . In previous works [4, 5], we determined all possible pairs \((N_q(C_A),I_q(C_A))\) , where \( N_q(C)\) and \( I_q(C)\) denote the number of rational points and rational inflexions on a curve C, respectively. The resulting pairs are: \((q\sqrt{q}+1, q\sqrt{q}+1)\) , \((\sqrt{q}+1, \sqrt{q}+1)\) , (1, 1), \((q-\sqrt{q}+1,0)\) , \((q+1,1)\) , \((q+1,2)\) , \((q+\sqrt{q}+1,1)\) , and \((q+2\sqrt{q}+1,0)\) . Extending these results, we aim to categorize the curves into equivalence classes according to their projective equivalence. It is well known that the curves of type \((q\sqrt{q}+1, q\sqrt{q}+1)\) are Hermitian curves, which constitute a single equivalence class. We focus on partitioning curves of other types into their respective projective equivalence classes.