Malwares are basically malicious software, which can be of different types including but not limited to virus, spyware, and worms or even Trojans. These are actually programs which cause harm to your PC.
Worms are malicious software programs which make copies of themselves over and over on the local drive, network shares, etc. The sole purpose of the worm is to reproduce itself over and over again. It doesn’t harm any information on the computer. Different from a virus, it does not require attaching itself to an already existing program. Worms spread by taking advantage of weaknesses in the operating systems.