bit.currency is market pegged asset (MPA) and backed by at least 200% collateral, ie. bitUSD and bitCNY. It is the most honest, trustworthy crypto-money on the planet and several Chinese exchanges are starting to replace Tether with bitAssets like bitUSD and bitCNY (https://www.aex.com/).

open.whatever is a user issued asset (UIA) created by gateways (such as OpenLedger) and is theoretically backed 1:1 by "whatever". So when you deposit 1 BTC via OpenLedger they issue you 1 open.BTC to go trade with on the DEX. This is exactly what Binance, Polo, Bittrex etc. do but Bitshares is honest and transparent about it.

Crypto-bridge (http://crypto-bridge.com/) is creating a decentralized gateway that solves the trust issue with gateways like OpenLedger, Rudex, etc.