It seems that invoking "xlnx,drm" directly in device tree was the old way of doing things. The actual name of this driver is xlnx_drv.c. From my understanding, this driver is used by the other various Xilinx driver pieces in order to create an overall DRM display device (which happens when you properly include and configure the other pieces of the pipeline properly).
https://xilinx-wiki.atlassian.net/wiki/spaces/A/pages/18842520/Xilinx+DRM+KMS+driver
If you notice, these individual drivers (like mixer) include the xlnx-drm driver and use its calls to actually create a DRM display device. Also, the various drivers may implement different roles of the display pipeline. Mixer implements a CRTC and planes while HDMI-TX, DSI, etc would implement encoder and often connector roles (in the HDMI case). See page 63 of the ZynqMP Targeted Reference Design:
https://www.xilinx.com/support/documentation/boards_and_kits/zcu102/2019_2/ug1221-zcu102-base-trd.pdf
My guess as far as xilinx vs. xlnx - xilinx is probably those drivers as they have been accepted by the mainline kernel tree (xlnx isn't in mainline) vs. the PetaLinux kernel ones. You will also notice they have different device tree compatible strings and the xlnx one has additional drivers as well. The ones you should probably be using are the xlnx/PetaLinux tree drivers.
