What is the difference between BitKeepSwap and cross-chain?

In one sentence: BitKeepSwap=DEX+Cross-chain, the cross-chain function is included by BitKeepSwap.

It is easier to understand from the transaction scene:
Ordinary Swap: support different currency transactions on the same chain
Cross-chain bridge: support transactions of the same currency on different chains
BitKeepSwap: Supports different currency transactions on the same chain, the same currency transactions on different chains, and different currency transactions on different chains
That is to say, as long as it is within the scope of the main chain supported by BitKeep, no matter what kind of transaction (cross-chain or cross-chain, the same currency) can be directly used BitKeepSwap function, and it is faster and more convenient than ordinary cross-chain.

If you really want to understand the difference between Swap (DEX) and cross-chain, you can read the following paragraph:
Decentralized cryptocurrency exchange DEX is based on blockchain technology. It is generally an application written on a specially adapted platform for smart operation of contracts, such as Ethereum. In this case, there is no institution to which we must entrust our funds. Transactions happen on the blockchain network, not on platforms that are stored on someone else’s servers.
When trading on such exchanges, we exchange cryptocurrencies with counterparties. For example, we can buy tokens by paying in ether. The ETH located in our wallet is transferred to the contractor, and the tokens in his wallet are sent to our wallet.
Asset cross-chain simply means that the coins of the two chains are sent to each other. But how? There are many cross-chain technologies for coins, such as two-way-peg, hash time lock, atomic swap, asset pledge transfer, gateway, federated signature and so on. These terms alone are enough of a headache, and each cross-chain method is worth explaining its principles in a large space, but you must be impatient to read and understand. In short, DEX and cross-chain are two asset exchange methods in different application scenarios. Let’s learn more later.