That is correct. If you install Flash from Adobe, it will install both the 32 bit and 64 bit versions for the selected browser type. Not sure why the control panel item specifically says 32 bit in the name.
I use Waterfox as my browser, which is a 64 bit browser. As you can see from the above picture, I have Shockwave Flash as one of my active Plugins.
I usually get my download from the link below
I then run the EXE or MSI for the browser type, and I'm good to go.
Note: Kill Cancer to Reply via e-mail