In order for a full-wallet to scan the blocks, it needs them locally. A lightwallet server is like a full wallet which exposes a JSON API for the products.

I think it just finds a random remote node to sync with, so you don't need to download the blockchain.. But I think the computation is still client-sided. Does MyMonero move the computation to the server, and this would be more like that?

How does this compare to running the GUI wallet in simple mode?

vtnerd rebased the free Monero lightwallet server C++ impl. Please review -let's get this thing merged so everyone can have cached, up to date transactions scanning