Yes, you can have both together on the same PC.
Usually, most people use the SSD for the operating system (Windows, Linux, etc.) and applications (Office, game launchers, browsers, etc.) while using the hard drive for game and personal file storage since games tend to be rather large and large SSDs are very expensive while large hard drives are relatively cheap.
The only problem with that is that while that makes the OS and applications much faster, it doesn't do anything for game map, level and startup loading times, but it's still definitely a good option since those usually don't take THAT long anyhow, and a few seconds won't kill anybody while something is loading.
Storage media has zero effect on "FPS" anyhow, so that won't be affected no matter how you use these drives.
If you're going to use an SSD for the OS my advice is always to do a clean install of Windows and then reinstall all your game launchers, browser and other applications as well, so that you are starting with a nice, fresh copy of Windows. You can however "clone" your current installation to the SSD if the total used space on your HDD isn't more than about 75% of the available space on the SSD. Clean install is better though.