Presents are items that can be found in The Pond. There are two types of pond presents, yellow and red. Red being the rarer of the two and the one containing more valuable items. They can contain consumables, frogs, coins, habitats, or scenery.
You do not have to accept a present in order for it to be counted in your Pond Presents total on the leaderboards.
The Puzzle game prizes are the same as the yellow (non-rare) presents.
Yellow Presents are common. It is unlikely, but possible, to get a rare frog, habitat or item from Yellow Presents. Frogs will almost always be at least one rarity level below the user's current level. There is an award for getting two Yellow Presents in one pond trip, "Gifted."
Red Presents are rare and can contain rare frogs and scenery, as well as larger amounts of consumables and coins. Even frogs that you haven't found yet, at the user's level. The higher your level, the better the contents of a red present, but low-level players can still find rare items. There is an award for getting two Red Presents in one pond trip, "Treasure Hunter."
The pattern for coins, potions, and stamps seems to be based on Ceiling (player level/2). You get this amount of potions or stamps, or 1000 times that in coins. For example, a level 21 or 22 player would get 11 potions, or 11 stamps, or 1100 coins.