Does Tradingusdt use a Binance wallet?

Yes, right, 

When you sign up for Tradingdusdt, a Binance account and a Binance wallet are created through API linkage.

[How to confirm Binance Internal Transfer]

1. For internal transfer within Binance and Tradingdusdt, no Txid will be created. The Txid field will be shown as [Internal Transfer] and the [Internal Transfer ID] of this withdrawal. 

2. The "Transaction Fee" displayed will be charged only for withdrawals to non-Binance addresses. If the recipient address is correct and belongs to Binance accounts, after the transaction the "Transaction Fee" will not charged. 

Further Information : How to Make Internal Transfer within Binance