According to dictionary.com, a model is a "representation, generally in miniature, to show the construction or appearance of something". For complex software projects, it is not unusual to either build a model as part of a prototyping process or include a data model as part of a specification.
A specification is a written document. Specifications may have specific purposes such as to document requirements, functional requirements, or designs. In an organization where the business requirements and technical requirements are separated, the design specification needs to be shared with the team developing the business requirements since they need to assist in the validation that the design meets the requirements.