OpenLedger it's like Bitshares wallet online, but you private keys are stored in Browser cache localy! 3rd party servers don't know your keys! And for this reason it is important to backup your wallet with your new account ASAP to bin file.
Lightwallet it is also browser based. You can download it here :

I understand ... I have run my own local server that connects to the OpenLedger's websockets (mainly because I was too idiotic to figure out how to get a full bts 2.0 node running).

I haven't participated in a dropshare before. All I wanted to know is if I could have my username already be created (which it is) and have (more) funds moved into my account and be credited during sharedrop, without having to go through the whole sign-up through OL.

In many ways bitshares accounts are handled in a similiar way as steem. Initial creation/registration requires a fee and new accounts must be registered by existing accounts. Currently openledger is the well known registration entitiy(similiar to but there are others, freedomledger is another one. You can also have someone you trust register the account for you and transfer it to a key you control.
Once you have the account you can access the bitshares blockchain through one of these web portals or run a your own local witness node. The node is very similiar to steemd and can be connected to a cli wallet or gui. Essentially once you have your account, you could do all your trading through your own local node.

I ported my username over from 0.9.x and run a light wallet connecting to the WS that OL provides. I just wanted to know how I would be credited if I deposit funds into the account that I control.