The nursing theory featuring the relationships described in the question, where the nurse and client work together purposefully with congruent judgments and actions to achieve goals, is the Theory of Goal Attainment and Transactional Process by Imogene King.
The nursing theory that includes the relationships described, where the nurse and client are purposeful interacting systems, and their perceptions, judgments, and actions lead to goal-directed transactions, is the Theory of Goal Attainment and Transactional Process by Imogene King. This theory emphasizes the importance of the nurse-client interaction and the dynamic process in which both parties work towards the accomplishment of goals through transactional communication and interaction.
In this theory, congruency between the nurse's and client's perceptions, judgments, and actions is crucial for effective communication and goal attainment. The process is collaborative, with both the nurse and client bringing their own knowledge, experiences, and resources to the relationship to achieve the desired health-related goals.