Viruses are an attack on your computer and change things in your computer and can make it so your computer can be used/controlled by others. Malware is just what it sounds like and what you experienced, people trying to get to "you" personally. They want you to buy their product or trick you into giving them your information, etc. Viruses just take it, you don't know they're there and they are more embedded in your machine, not just a single piece of software.

Malware usually comes from surfing the Internet, going to certain sites or investigating what looks like a legitimate ad or downloading "free" stuff. It is similar to some viruses that way but since it isn't trying to get into your computer innards through ports and down deep stuff, the virus protector doesn't "see" it. It's stuff that you "willingly" click on and "ask" for. It can be as nasty as virusware but can't go to someone else's computer, doesn't look at your files, just embeds itself in a single program usually. Often if you uninstall that program and reinstall it, that gets rid of the problem. But there's other not obvious malware (people tracking where you're going on the internet and what you're looking at so they can better see how people behave on the internet but, unlike some people/sites that ask your permission to do this, malware does not ask, just does it and you don't know either what they are studying the data for or how it impacts you).

The really ugly malware that asks for or gets information from "you" (rather than taking control of your machine) is known as "phishing" and I'm sure you've gotten junk mail telling you you've won something or that your bank account has quit working, click on this link and we'll fix it? That's trying to get YOU to "willingly" click on the link (like writing stuff in contracts in small print) and give them information so they can steal from you. "Mal" stands for "malice". It's ugly and wants to hurt YOU rather than your machine. It's also called spyware (spying on you and what you're doing).

Viruses send themselves to everyone in your email account, for example. My niece's daughter had a problem with that on Facebook, someone got in her account and her account started sending out pornographic links saying they were from her with things like "Look at this!" for the subject and, since she's a young girl, friend/relative people would click on it and it would come to their machine and then send out the same links from their email accounts. Mostly, viruses are used to "control" your machine in the middle of the night, say, when you don't realize it. That's why you should turn off your machine when you're not using it. If someone has a virus they control on your machine they can send things through your machine that makes it look like it is coming from your machine. That's how spam works and why email accounts, no matter how good, can't get rid of all spam. It's untraceable because it's going through so many other machines you can't find out where it started, who's doing it.

Some "obvious"/big viruses can be stopped by virus software but bad guys are constantly thinking up new bad viruses and the protection people have to get "caught" by a new virus before they can protect against it. That's what's behind all the "crashes" you hear about and the credit card thefts, etc. There's hackers trying to get at the machines and what they contain. Some efforts are more serious than others, none of them are any good.