Whatever your conceptual relationship to plan and planning, many of us have connotative differences in how we experience these two words.
A plan feels like something to follow. It's object existence contrasts with the verb life of planning, which feels more alive and adaptive as all living things express. It even feels somewhat awkward and inaccurate to call the documentation in planning as "a plan." That's why we use the term canvas for our agile approach to planning. Canvas implies something you keep working and reworking in the process toward to satisfying outcome.