I would d/c the hdd from power while installing win 10 on ssd as Windows will see the boot partition on hdd and use it instead of making a new one on ssd. The problem with it doing this is if you later remove hdd, the ssd won't boot.
I suspect installing win 10 on a PC that already has it installed will likely see 1 of the 2 installs marked as default and PC will ignore the other one. This won't happen if you remove hdd from power before installing as then UEFI bios should know which drive to boot from.
It kind of depends on which format the drives are using.. MBR or GPT. If its MBR, then which boots 1st would depend on boot order. If GPT, it depends which is recorded as 1st in line by the BIOS