So if my understanding is correct "cross chain trading" is a decentralize exchange between different blockchains, while what people called right know "decentralize exchanges" are only decentralize exchanges within a sole blockchain, am I right?
Yes. However Mastercoin and Counterparty allow for a fully decentralized exchange with BTC, because they just implemented their protocol on top of BTC. That said, it limits them severely (high transaction cost, high confirmation times, etc.)
UPDATE: I think it's easy to do cross chain, if we just include the hashes of the main BTC blocks, and then only include the blocks that had relevant cross-chain transactions, it could be implemented in BTSX.