The wedge key is the standard chroma key method, using a colour vector angle to remove the colour for a chroma key. This works great under ideal conditions. However, if the scene includes high detail luma content in edge regions, these may not be included in the output.
The detail key can develop subtle video and alpha shapes to discriminate high detail luma content in edge transition areas. This is great for retaining high-resolution edges but can cause issues when background and foreground levels are similar within the video itself.
These 2 modes can be combined for optimal capture of high luma detail in the edge regions, as well as compensation for similar foreground and background levels.