The short answer is: none. Facilitation guides and lesson plans are two terms used for the same thing. They are the detailed guides that an educator can use to implement a specific strategy. So, for example, if I were going a study skills workshop, the lesson plan or facilitation guide would list the specific outcomes that one is hoping to achieve during the workshop, how these outcomes map back to your overall curriculum goals and outdoors, details what would need to be prepared to execute the workshop, suggestions on how to facilitate it, and the assessment measures that will be used.
Whether you choose to use the term facilitation guide or the term lesson plan is up to you. Typically this choice will be informed about your campus culture and what makes most sense in your context. Some may wish to use the term lesson plan, because it helps staff make the mental connection that it is similar to what a teacher may develop for a classroom lesson. Others may wish to use the term facilitation guide as it tends to seem more collaborative and less didactic.
I recently came across a webinar on the curricular approach where the presenters stated that there is a “big debate” over whether to call it a facilitation guide or a lesson plan. I’m not aware of any debate on this topic, and I would actually argue if you perceive it as a debate, you’re focused on the wrong thing. Words matter, but if you’re overly focused on the language, you’re missing the more important intent and design of a curriculum. As long as you choose a word, and apply it consistently in a way your entire team understands, then that’s all that matters.