Academic and non-academic writing usually differ in format, purpose, and tone.
Popular forms of academic writing include essays, themes, research studies, and similar structured pieces. Academic writing includes an introduction, an overview of the topics discussed within the writing piece, and a conclusion which wraps up any final thoughts. In scientific fields, including social sciences, writing is often in the form of research papers, and may include an abstract which summarizes the thesis and findings of the research which it discusses. Non-academic writing does not need to cohere to these standards of layout, and may take any format.
The purpose of academic writing is usually to inform the reader, providing non-biased facts and backing up claims with evidence. In the field of literature, an academic may write an essay based on a theory, but shows how the theory can be proven with evidence from the literature he/she discusses. The purpose of non-academic writing may be to entertain its audience or to persuade the reader.
Finally, the tone differs. In academic writing, the tone should be formal and professional. There are guidelines such as keeping the writing in 3rd person and eliminating contractions. Again, the writer attempts to present a point without bias or opinion. In non-academic writing, the tone may be informal. Non-academic writing does not have to cohere to the guidelines of formal writing and may include humor, opinion, or other elements not present in most academic writing.
Although these guidelines are not concrete, and depend largely on subjective differences, academic and non-academic writing usually differ in format, purpose, and tone.