You can play different versions of Minecraft on your Quest. However, the process is a little different. You will need to buy one of the versions if you don't have the other.
These are the Minecraft versions you can play on Quest.
Windows 10 (Bedrock), edition: This version of Minecraft can be purchased from the Microsoft Store. This version has VR capabilities and can be set up quickly. However, it can't be modified in the same manner as the Java version.
Java edition: This is the original Minecraft version that comes with tons of mods for free online. Although it is more difficult to get this version running in VR because you will need to install Java, Steam and Steam VR if not already done so, the implementation is much more fun. You can, for example, mine bricks by swinging your controllers.
How to play Minecraft Bedrock Edition with Quest:
Search for Minecraft and choose it from the results.
Click Free to Install.
This is not the full Minecraft app. It's just a free program to allow Minecraft Bedrock Edition in VR on Meta/Oculus hardware.
Wear your headset and connect it via link cable to your computer.
Enable Oculus Link to be enabled.
Find Minecraft in your apps, search for it and then select Start.
Minecraft will launch VR.
Install Java, Steam, and Steam VR to play Minecraft Java Edition on Quest. Before you proceed, ensure that you have all three installed.
How to play Minecraft Java Edition on Quest:
Go to Vivecraft's Download Page and click the most recent version of Vivecraft.
Click vivecraft-x.xx.x-jrbudda-x-x-installer.exe and download the file.
Click the Install button after the file has finished downloading.
If Java is not installed on your computer, the installation will fail.
Open the Oculus app from your computer.
Wear your Quest headset and connect it with a link cable to your computer.
Open Steam VR on your computer and click Launch.
Select the monitor icon in the Steam VR interface.
If you have more than one monitor, choose the one that Minecraft will run on.
Minecraft will not display on your virtual desktop if you choose the wrong monitor. You can either choose another monitor or repeat the previous step to select the correct one.