How to Transfer Steam to a Different Harddrive on the Same Computer
If it's about save data, you don't need to worry about that. Not with Fallout 4, anyways.
Fallout 4 is compatible to the Steam Cloud, which means your PC will automatically download them if they are somehow missing. In fact, you could even play the game on 2 different PCs and their progress would be synchronized.
Even if you're not using the Steam Cloud, Fallout 4 saves its progress to your personal Documents folder, which is on C:\ by default. Moving Steam won't affect it. In addition to that, Windows 10 can move your personal folders (including the Documents folder) to OneDrive, which is also a Cloud service.
As for moving Steam, I wouldn't do that. You'd likely have to reinstall Steam in order to not mess with the Registry.
Luckily, Steam supports installing games outside of the Steam installation folder. The feature is called "Steam Library Folders". Simply create a folder on your SSD, and have Steam move your games to the new folder. Note that some games (especially old ones) might not support being moved to a Steam Library Folder.
To create a new Steam Library Folder:
- Open Steam.
- Click "View", then "Settings".
- Select "Downloads", then click on the "STEAM LIBRARY FOLDERS" button.
- Click on the "ADD LIBRARY FOLDER" button, create a folder on the SSD (if you haven't already done so), and select that folder.
- You can delete the new folder, or set it as the default installation folder by right-clicking on it and selecting the appropriate option.
To move games to the new Steam Library Folder:
- Open Steam (if you closed it).
- Right-click on the game you wish to move, and select "Properties..."
- Switch to the "LOCAL FILES" tab, and click on the "MOVE INSTALL FOLDER..." button.
- If you have created more than one new Steam Library Folder, you may choose which folder to move the game to.
Just copy the Steam data folder to the new disk, and tell Steam about the new location on the new disk. 
Restart Steam and enjoy more speed.