Stamps → Actually "Stamps" don't exist. The game uses:
Medals: Bronze/Silver/Gold/Platinum per sport event (Swordplay, Wakeboarding, Frisbee, Archery, Basketball, Table Tennis, Golf, Bowling, Power Cruising, Canoeing, Cycling, Air Sports).
Stamps (Mii Plaza / StreetPass): Unrelated—StreetPass Mii Plaza gives puzzle pieces/stamps for meeting Miis.
Resort Pass: Unlocks islands/areas as you earn medals.
3. Wii Sports Club (Wii U)
Uses "Stamps" for daily challenges (one per sport per day). Collect 7/week → Mii outfit.
If you're seeing "Stamps" in Wii Sports Resort, you might be misremembering Wii Fit or Wii Sports Club. The core reward loop is Medals → Resort Pass progression.