It really depends on how you have decided to move your OS, @andP. If it's the cloning process, you should keep the HDD intact until the procedure has been completed. Afterwards, check if your SSD will boot successfully while having the HDD unplugged from the motherboard.
If it is successful, make sure you edit your BIOS settings and put the SSD into first-boot priority (instead of the HDD) and also set the SATA mode for the solid-state drive to AHCI.
You can easily use the HDD as well after that, it's just that you need to backup the data from it beforehand to keep your peace of mind about the integrity of your files. Turning your SSD into the primary/booting storage will require you to delete and erase all the programs and the OS installation from the old hard drive. You can
execute the formatting procedure through Disk Management. Afterwards, you will have a completely blank secondary HDD which you can use however you like. You can transfer back all your essential files from the backup and install new programs and software on it. Just make sure you check the third tutorial about changing the default install path to the HDD, instead of filling your SSD with random data.
Check the tutorials I shared with you and see if there's anything unclear about the whole procedure.
SuperSoph_WD