TL;DR Bitshares is the original Decentralized Exchange and Blockchain. Openledger, RuDEX, Crypto-Bridge, GDEX etc are gateways using the Bitshares Blockchain.
Bitshares is a Decentralized Exchange (DEX). That means all orders, order matching and transactions are done on the blockchain using smart contracts. The thing about blockchains and cryptocurrency is, anyone can run a node, see and interact with APIs. Bitshares makes it very easy to read market history, asset information and place orders for users.
Openledger and other such websites are gateways, providing a front interface to the Bitshares Blockchain. Orders and transactions still happen on the one and only Bitshares blockchain, so each gateway helps increase liquidity.
However, if you’re accessing a gateway instead of Bitshares, make sure the website URL is correct and you’re not visiting an imposter website.
Gateways can also offer their own assets, e.g. OPEN.BTC, BRIDGE.LCC, OBITS, BCO. These have their functions. E.g. OPEN.BTC and BRIDGE.LCC are IOUs so 1 OPEN.BTC is a promise that OpenLedger will hold a Bitcoin for you, which you can claim back when you’re withdrawing from the Bitshares blockchain. Similarly OBITS gives a monthly dividend to its holders, and BCO pays back depending on your stakes in the Crypto-Bridge gateway.