Malware is a short term coined for Malicious Software, the google definition of which is “software which is specifically designed to disrupt, damage, or gain authorized access to a computer system”.
Malware is capable of stealing, encrypting, or deleting sensitive data on computers, they can also be used to monitor your activities, without your permission.
Malware is a very broad term, it includes other sub-types like-Virus, Trojan, Worm, Spyware, and the latest all ransomware. All of these are a type of malware that affect the system in various ways.
A virus is a specific type of malware that can affect the system. It may be a piece of code in software that performs unwanted activities and can spread itself. Virus and worms are kinds of similar, as per my understanding, the virus is something that doesn’t propagate on networks but a worm does propagate on the network and affects as many systems as it can.