Based on the terminology I was taught:
A commissioning plan is an exhaustive / comprehensive plan for completely proving the full functionality of a new build of any kind, including that the correct settings are applied to all alarms, trips, control ranges, et cetera and so forth, performing pre-run end-to-end checks to confirm that all wiring and functionality can be proven while still in the "cold iron" state and in advance of initial first-time-ever actual live plant operation, and also for sequentially testing that, with the plant in actual operation, each and every control / alarm trip point actually controls / alarms / trips for whatever it's supposed to.
A start-up plan is the documentation based upon a known plant configuration and behaviour that incorporates all pertinent limitations on warm-up rates, etc., etc., and is the plan used in start-ups during normal/routine operations once a plant has been fully commissioned.
If "startup plan" is actually meant to mean "initial plant start-up plan", all bets are off...
CR
"As iron sharpens iron, so one person sharpens another." [Proverbs 27:17, NIV]