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So there is virtually no difference between the two. Vius is just another form of Malware that maliciuosly affect system performance and get spread across systems through a shared files.
Virus are specific type of malware, Malware is a broad term used to describe all sort of unwanted malicious code
Malware means a malicious software to harm the host system and virus is a kind of malware similiar to adware,spyware etc which spreads itself once run.