Do you mean from a CF to a SD (secure digital) card?
You can do that. They are usually formatted using the FAT (FAT-16) file system. (you can check by plugging one in your card reader and checking the properties.)
For regular data or just photos for storage, you can plug both in your multi card reader, copy the files to a temp folder on your HDD, choose the ones to copy over, then copy or drag and drop them onto the other card. Could copy files from a flash drive to a CF card also if desired for storage or transportation.
Most cameras use sub folders to record photos taken, for example a Canon might use DCIM\100Cannon to store its images. You can obviously copy those jpg images to your computer, and can store jpg files in those subfolders also, but the camera may not know how to handle a jpg that is a different size than it regularly records or other image file type like png images.