Right now everything you installed is on one drive, so everything is setup in the registry under C drive. Now you'll have 2 drives, with saved games, steam main files, etc on C but the actual game files, long term storage, associated other stuff will be on D (hdd). If you pdid a straight swap and only had the one drive, the clone would be best, but having 2 drives, the pc will not find anything, bunch of dead ends, missing files etc.
So yes, you'll need to reinstall all the software, you'll install anything you want on hdd, but it'll automatically link and install anything it needs (like drivers etc) on C. That way when you click on the shortcut to start the game, it does all the linking with windows, drivers, game files, steam, etc between the 2 drives.
When doing a fresh install of windows, you only want the OS drive plugged in. If you have both, windows will seperate to install partially on both, which is a pain to fix. You want windows as an OS in one spot, it'll find D all by itself later without being attached to it.
Once windows is in, you hook up the hdd and boot. Since both now contain a bootable OS, just pick the ssd when it asks. Then you can transfer anything in documents, downloads or anything else that's a loose file, like emails etc from the hdd to the same folder on the ssd.
When you've moved everything that you want to keep, and double checked, and checked again, go to windows start/search and type in hard disk partitions. Then follow the wizard to partition the hdd as a single, simple drive. This will remove everything like a format would, but will also reset the hdd so it's just storage and not a boot drive.