Bylaws are an organization's foundational rulebook. They cover the PTO's purpose, membership, officer roles, voting procedures, and how meetings are run. They're formal, carefully written, and changing them requires a vote of the membership.
Standing Rules are more day-to-day and practical like meeting schedules, budget procedures, or how committees operate. They're easier to update than bylaws and handle the details that keep the organization running smoothly from year to year.