Characters
The leaderboards rank the Inferno clear times of every region's boss stage (stage 7; Spire Hill Crypt Lower: stage 3), plus the Mythic Rift, with a tab per hero. Online characters take part in them.
Character slots
The main menu has two tabs, "Singleplayer" and "Online"; each tab shows 4 character slots. Singleplayer characters cannot use the leaderboards or Market Trading; creating one asks first:
"Singleplayer characters cannot use social features such as Leaderboards and Market Trading. Continue?"
"Online characters can participate in leaderboard, trading and other social features. Stable network is required for the best experience. Violating online policy could result in ban."
"Only online characters can trade." The Auction House is for online characters only.
Online characters cannot buy equipment or treasure chests in a shop ("Gear can't be bought on online characters", "Chests can't be bought on online characters"). They can buy Mystery items, at the price the game server sets.
Auction House items that are withdrawn or claimed arrive in the mailbox: "Withdrawing or claiming sends the item to your mailbox after a short cooldown."
Storage, gold, materials, Life Skills, unlocked minions and Paragon.
Statistics
The Statistics panel counts Total Play Time, Total Gold Earned, Total EXP Earned, Deaths and the loot found of each rarity.