HDR
High dynamic range (HDR) represents a wider luminance range than standard dynamic range (SDR), allowing bright highlights alongside darker detail. To understand the result, consider the content, the display's capabilities and the output mode together. None of those alone tells the whole story. Apple’s HDR overview
Apple's extended dynamic range (EDR) rendering can represent values above ordinary SDR white. XDR, or Extreme Dynamic Range, is Apple's naming for supported displays and presets; it does not mean that every HDR display behaves identically.
BetterDisplay separates an HDR output mode from software XDR/HDR upscaling. Upscaling raises ordinary desktop content into available brightness headroom. It can make that desktop brighter, but does not turn SDR material into content originally mastered in HDR.
HDR can also change which hardware brightness controls work. See Brightness and Nits for the adjustment methods and luminance units. Software XDR/HDR Upscaling and Dimming explains the relevant settings.
SDR and XDR
Standard dynamic range (SDR) uses a conventional reference white and a more limited luminance range than HDR. Extreme Dynamic Range (XDR) is Apple's display naming, rather than a universal signal format that every monitor implements.
Brightness upscaling uses available headroom to raise the brightness of SDR desktop content. Its purpose differs from resolution upscaling, which increases image dimensions. See EDR and brightness headroom for the relationship between SDR white and available peak brightness.