The $\text{LaAlO}_\text{3}$/$\text{KTaO}_\text{3}$ system serves as a prototype to study the electronic properties that emerge as a result of spin-orbit coupling. In this article, we have used first-principles calculations to systematically study two types of defect-free (0 0 1) interfaces, which are termed as Type-I and Type-II. While the Type-I heterostructure produces a two dimensional electron gas, the Type-II heterostructure hosts an oxygen-rich two dimensional hole gas at the interface. Furthermore, in the presence of intrinsic spin-orbit coupling, we have found evidence of both cubic and linear Rashba interactions in the conduction bands of the Type-I heterostructure. On the contrary, there is spin-splitting of both the valence and the conduction bands in the Type-II interface, which are found to be only linear Rashba type. Interestingly, the Type-II interface also harbours a potential photocurrent transition path, making it an excellent platform to study the circularly polarized photogalvanic effect.