There are two varieties of JRE available. Java VM: IBM vs. Sun.
Is there a way to know which JRE I am using through JavaScript or some Java issued command.
Git Bash + Windows 10 + Software that came bundled with its own JRE copy:
Do a "Git Bash Here" in the jre/bin folder of the software you installed.
Then use "./java.exe -version" instead of "java -version" to get the information on the software's copy rather than the copy referenced by your PATH environment variable.
Get the version of the software installation: ./java.exe -version
JMIM@DESKTOP-JUDCNDL MINGW64 /c/DEV/PROG/EYE_DB/INST/jre/bin
$ ./java.exe -version
java version "1.8.0_131"
Java(TM) SE Runtime Environment (build 1.8.0_131-b11)
Java HotSpot(TM) 64-Bit Server VM (build 25.131-b11, mixed mode)
Get the version in your PATH variable: java -version
JMIM@DESKTOP-JUDCNDL MINGW64 /c/DEV/PROG/EYE_DB/INST/jre/bin
$ java -version
java version "10" 2018-03-20
Java(TM) SE Runtime Environment 18.3 (build 10+46)
Java HotSpot(TM) 64-Bit Server VM 18.3 (build 10+46, mixed mode)
As for addressing the original question and getting vendor information:
./java.exe -XshowSettings:properties -version ## Software's copy
java -XshowSettings:properties -version ## Copy in PATH