When writing an essay there are many requirements from the instructor on how to format your work, whether the assignment should be written in the first, second, or third person, and even the parameters with which to write. The words "style" and "format" are often confused due to these requirements. I hope this helps clear things up a bit.
Style refers to the actual writing perspective and purpose of the work. For example, the requirement that your work be a research paper and should include a large amount of researched data would be a style requirement. Another example would be a requirement that you describe an experience you have had (or assigned experience for the class) from the first person. Normally, using "I" or "me" while writing is considered improper and lazy, however, in this case, the instructor is trying to get you to write your experiences more creatively and is giving you room to work with by allowing you to write in the first person.
Format refers to the actual structure of the essay you are writing. APA, MLA, and Chicago Style are all guides that are used for formatting. For example, if your essay needs to be double-spaced (and most do) this would be a formatting requirement. Another example would be the need for one inch margins and a running header.
So, as you can see, the terms "style" and "format" are easily confused, but their meanings are incredibly different. As always, refer to the grading rubric for your work and remember that there are tutors waiting to give you advice and guidance when you are stuck. Happy writing!