These terms are indeed open to a lot of interpretation. As a result you and your team need to gauge user expectations.
Low fidelity mockups are created to gauge the usability of the product. You're trying to find out if the users understand, and are able to use, what has been designed. You are getting feedback not on how pretty it is but on how well your team has grasped and accounted for the use cases.
Example: You walk through a scenario with a user. He's already logged in and is now working on a specific task that has multiple steps. Your mockup should allow him to go from step to step. Your role here is to see if it's intuitive.
Do the users navigate through the steps easily? What are their questions? Can you use these questions to generate as of yet unstated use cases.
Often times at this point new use cases; new requirements are verbalized. This is not necessarily a case of mission creep, it's simply that when the users see their ideas in action they realize that several important requirements were missed.
In short this initial mockup should be as quick and easy to create as possible and yet - at the same time - give a realistic feel of an application.
Only after this set of broad level of analysis is done do you get into higher level mockups.
Every business, every agency will have a different set of user expectations.