Conceptual Design is an early phase of the design process, in which the broad outlines of function and form of something are articulated. It includes the design of interactions, experiences, processes and strategies. It involves an understanding of people's needs - and how to meet them with products, services, & processes. Common artifacts of conceptual design are concept sketches and models.
A concept study (conceptualization, conceptual design) is often a phase of project planning that includes producing ideas and taking into account the pros and cons of implementing those ideas. In fact, this step is often termed Ideation or "Concept Generation."
Conceptual design is the very first phase of design, in which drawings or solid models are the dominant tools and products. The conceptual design phase provides a description of the proposed system in terms of a set of integrated ideas and concepts about what it should do, how it should behave, and what it should look like, which will be understandable by users in the manner intended.