So pgAdmin III uses C++ and wxWidgets and pgAdmin 4 uses web-based technologies?
Yes.
That's interesting but the question is, will there be a pgAdmin 5?
It's not impossible. There have been 3 other complete rewrites over the last 28 years after all (4, if you count to original rewrite of pgManager to pgAdmin I).
If a web based model is the future, then why shouldn't we say pgAdmin v10 or simply pgAdmin 10?
In another 50 years we might - and I say that only half-jokingly, as I certainly didn't expect pgAdmin to still be an active project with millions of downloads after nearly 30 years. Will pgAdmin be around in another 50 years? I doubt it, but I'm not going to definitively say no.
My question should lead to another question: Will there be a pgAdmin 5?
Maybe - who knows what the future will hold, or what technology changes might force another rewrite?
in most cases pgAdmin 3 is too old therefore pgAdmin 4 is the most use tool for postgres. it's confusing if you write pgAdmin 4 and then the version number.
it should be able to understand what pgAdmin 9.7 means. it means pgAdmin 4 in the version 9.7. I suggest you to change the name of pgAdmin 4 at least in version 10.
so instead of pgAdmin 4 v10 simply write pgAdmin 10.