I’m still on the waiting list for Argent and their website doesn’t tell me much about that topic within a 5 min search. Zerion uses 0x and kyber as decentralized exchanges. In both cases the user of the wallet remains in full control of their assets, since these exchanges operate with on-chain contracts in contrast to centralized exchanges like Bittrex, Coinbase etc.
This crypto to crypto trading feature is more or less getting standard due to the fact that kyber (as well as other DEX platforms) offer good interoperability and easy integration for wallet providers like ImToken, Enjin, Coinbase wallet, trust wallet, status etc.
However, to be honest I still struggle to classify access tools like mycrypto or MEW. They offer client-sided wallet services via a browser, but we should differentiate here as well. Since these services operate within the browser it’s probably best to call them “browser based wallet software”
So in the case of MyCrypto they offer a browser based wallet software via their website as well as a desktop based wallet software (My crypto desktop app)
I’m well aware of the fact that these are rather descriptions instead of a good naming scheme.