A design is a model without any implementation-specific or technology-specific details. A model is a design with those details.
There is a very sharp distinction between the two determined by the fact that users of a system only ever see its design whereas implementors are most interested in the model details.
Physical modelling not only allows designers to explore and test their ideas, but to also present them to others. Engaging clients focus groups and experts to interact with physical models of products allows designers to gain valuable feedback that enable them to improve the design and product-user interface.
The software that can be used when designing something to be 3D printed is entirely dependent on what you are trying to make. In general, 3D design software falls into two categories. CAD software is usually used when creating industrial objects such as mechanical objects. On the other hand, some CAD software enables more artistic freedom as designs do not need to work mechanically, be functional or fit to a real world device. Historically, 3D modeling software has been used in film animations and video games to make organic designs. However, it can also be used to create 3D printable models.
3D printer essentially works by extruding molten plastic through a tiny nozzle that it moves around precisely under computer control. It prints one layer, waits for it to dry, and then prints the next layer on top.
In the current scenario, 3D printing has been used in manufacturing, medical, industry and socia sector sectors which facilitate 3D printing or Additive Manufacturing to become successful commercial technology. More recently, 3D printing has also been used in the humanitarian and development sector to produce a range of medical items, prosthetic, spares and repairs.