The generally accepted definition of procedure in a Lean company is that it is the “how” of an operation. It is closely related to the term “process”. A process would be the series of steps required to complete the operation, or the “what”.
Think of the acronym SOP, which is either standard operating procedure or standing operating procedure. In either case, the “P” stands for procedure. Most people understand that an SOP is a description of how to accomplish a task. Closely related to SOPs are work instructions. These are part of Standard Work documentation.
The truth is though, the distinction is mostly semantic. It can be distracting to an organization to quibble over this sort of thing. The important thing is to make sure you have a well-documented set of instructions to accomplish the work in your organization. How you label it is not as important, though the whole organization should call it by the same name.
There are occasional cases, however, where it might be important how you refer to the steps of your work. For example ISO9001 uses specific meanings for the terms.