https://ardor.tools/ is a block explorer for Ardor testnet. Ardor main net is scheduled for launch about the end of November.
The ARDR tokens that were distributed after the three-month snapshots last year, and that are currently traded, are assets in the Nxt blockchain, so you won't see them in the Ardor testnet. Your account shows it has received 9.22 ARDR in the Nxt block explorer - https://www.mynxt.info/account/848572254977623952 - so probably the difference is due to Bittrex fees.
This is also the reason why your Ardor beta wallet does not show them. The current Ardor beta is working on testnet (and using testnet Ardor tokens, with no market value), while your ARDR are in the Nxt blockchain. NXT-53WJ-Z3A5-LAZC-2VPKR is a Nxt address.