The ransomware they're talking about is where all of the files on your computer, except those required for it to boot up, get encrypted. This is all done in the background without your knowledge and then, one day, your screen contains a message informing you what has happened and demands a fee (via bitcoin) to get the 'key' to decrypt the files. All of your documents, pictures, etc., are unusable.
In a properly-designed system, this is relatively easy to undo. Paying the ransom may also work, although you have no recourse if it doesn't. An offsite backup, updated regularly like daily, is an excellent defense even in an improperly-designed system for things like this as well as other conditions such as hardware failure.
What you're talking about is a rogue websites that force a popup on your screen, sometimes with accompanying audio, that says your're infected and to call a number. These are usually benign and what you did to get rid of it is the way to resolve it (or just kill the browser's process.) These rogue links are circulated via spam email and especially in social media. If you do call the number, it goes to an indian call center where they offer to 'fix' it for a fee. They have a complete shtick that includes a remote support session, doing things that bring up lots of numbers on the screen, and proclaiming, "See? You're infected!!11!" They do have the ability to cause damage during one of these remote support sessions, but usually all they want is scare you into buying their unneeded "protection software."