Hopefully as a professional java developer I can help you here. First of all if your not developing (compiling) your own java code then all you need is a JRE. As to the version you need - that rather depends on the .jar file you are trying to run. Whoever created it will have used a particular version of Java and you would normally need to run the same or newer version of Java on your machine. Having said that when Java moved from version 1.8 to 11 there were quite a lot of changes and some older java jar files might not work correctly.
Finally - licensing. Oracle took over from Sun when it comes to the ongoing development of Java and for some time they used to provide their java for free. The last version I recall which is free is 1.8 (202) - however don't panic - you can still use any of the open source versions of java.
You can download whichever version you need from here
https://adoptopenjdk.net/releases.html
If your unsure as to the version you need maybe you can let me know where the .jar comes from - hopefully the source of the file might indicate which java version to use. The bulk of .jars still use 1.8 at the moment.
So in summary - if your only running the java application you only need the JRE. If you think you might do some changes and re-compile the code then you are looking for a JDK.
I thought I read somewhere that the original Apple JRE no longer works in Big Sur - I certainly would not use it now as it's too old. Go for one of the downloads in my link above.
If you want to verify the default version of java being used on you machine, open up a command terminal and type
java -version
Hope this helps
Dave