There are three primary differences that separate the LLM resume from resumes for other programs: the ordering of sections, the inclusion of additional sections, and the overall length of the document.
1) Ordering the Sections on the Page
Your academic background and performance is a very important part of your overall LLM application. In some cases that I have seen it is even more directly related to the LLM experience that recent working experience. For this reason, I have often suggested to former clients that they emphasize their academic accomplishment by featuring the education section at the top of the resume, just underneath the contact information and before the professional experience - even if this puts the entire document out of reverse chronological order. The difference may not seem like a lot - after all both education and experience will appear in the document - but the impact is to me strong and especially so for applicants with a strong academic background. Reordering in this way can lead to a very good first impression for the resume reader.
2) Inclusion of additional sections
The LLM resume should be made up of the same sections that would be found in a normal resume, namely: contact information, education, professional experience and additional. However a strong LLM resume can also include additional sections, each of which add value by being relevant to the academic rigors of the LLM. These sections can include Academic Publications or Academic Presentations. Each will give the reader a strong understanding of the applicant's academic experience. They can also help the reader to see the particular legal fields in the which the applicant has academic experience or focuses on in their work.
I feel strongly that a good resume is a 1-page document, as I have written before. I feel the same is true for the LLM resume: a strong presentation of professional and academic skills is best done over one single page, where just the most relevant accomplishments are included. A resume that goes slightly over 1 page can be cut down by reformatting or simply removing some additional section contents (which are sometimes less important for LLM applications). However, I have in my experience seen some applicants with enough content spanning education, professional experience, academic publications and presentations to warrant a 2-page document, and so certainly the resume can be formatted to achieve this in a way that is pleasing to the eye and easy to read.