The way this blog post words it, at the very end of the post specifically, you need not re-download the HCW from either place. Instead, you do that once and then every time you run it later, just run it from the installed shortcut. It'll update itself automatically if a newer version is there (within the same major build).
So if you go and click the link in the EAC, it makes sense that it installs the version that is there.
So this is two issues - one issue is that Exchange team are having two different versions available in two different places. The other is customers re-downloading from both places and getting surprised that the version is different.
I would just use the external link for v17, then just relaunch it from the installed shortcut or return to the same link, but if going the latter route, keep going back to the same link.
Exchange has always been a big customer booby trap like this. Everywhere you look there is something odd that you just have to deal with as the customer. This is the product that first refused GUI items in favor of PowerShell, after all. So it's love hate for all.