Bitcoin Core and Bitcoin-Qt are two terms used interchangeably to refer to the same software, which is the original full-node Bitcoin wallet software. However, there is a difference between the two terms in terms of their usage and history. Bitcoin Core is the official name of the software that includes the wallet and other components, such as the Bitcoin Core daemon and command-line tools.
It is a reference implementation of the Bitcoin protocol and is used by many developers and power users for its advanced features and functionalities. Bitcoin-Qt, on the other hand, is the name of the graphical user interface (GUI) component of the Bitcoin Core software.
It is a user-friendly interface that allows users to interact with the wallet and manage their Bitcoin transactions and balances without needing to use command-line tools. In other words, Bitcoin-Qt is the graphical user interface that enables users to interact with the wallet, while Bitcoin Core includes the Bitcoin daemon and other components in addition to the GUI.
However, in practice, the terms Bitcoin Core and Bitcoin-Qt are often used interchangeably, and users can download and use the software under either name.