When we write about the “player” in Shotcut, we are taking about the part that looks like below.
When you open a media file (or generator or device in Open Other), it opens in the Source player. It is called “Source” because it can be the source of edit operations in the Playlist or Timeline. The Project player is the preview and playback controls for the Timeline (or Playlist if you are not using the timeline or for advanced users).
While all other parts of the UI are panels that can be moved or made to float in a separate window, the player cannot currently. Also, currently, the two players are only available as tabs and not side-by-side like some other video editors. You can adjust the size, however, by adjusting the surrounding panels and the size of the main Shotcut window.