A PC manufacturer's recovery disk will only return the computer back to how it was when new.
A system (or disk) image is a complete copy of a hard disk partition. That image is contained in a single file. Providing that you imaged your system (usually C:) drive, it contains the boot files, operating system, programs and user data. If you run into problems that you can't fix, or your computer's been rendered unbootable, you can restore the image and your computer will revert back to how it was when the image was created.
A backup is usually a copy of important files such as documents, e-mails, photos, and music etc saved to an external hard drive, memory stick, or CD etc. An image file can sometimes be classed as a backup because it's usually possible to extract individual files and folders from it.
A system image is likely to be bigger than a recovery disk because it also contains all the extra programs you installed and also your data files.