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In this work, we concern with the soliton solutions to an optical twin-core coupler that occur with four sorts of nonlinearities viz. Kerr law, power law, parabolic law, and dual power-law nonlinearity. The twin-core couplers with the nearest neighbor linear coupling are considered and bright, dark, and singular optical solitons are extracted with the aid of the integration algorithm of the new mapping method. The appropriate constraint conditions are naturally emerged to secure the existence of these solitons. For physical classification of the newly acquired solutions, we have expressed them graphically to describe the physical interpretation of distinct shaped solutions more evidently.