The English language being what it is, words and their usage are constantly evolving. I grew up referring to what I was playing on the Nintendo as video games (two words), but it is becoming increasingly common (and accepted) to see the term written as videogames (one word). I personally don’t agree with that particular change, but it is something that I have observed. Similarly, while it is standard practice to capitalize Internet, use the lower case internet is generally accepted too.
For now, and this may change in the future, the terms “backup” and “back up” are not interchangeable.
A backup (one word) is a thing. It is used as a noun. For example, I once wrote about the importance of having a backup computer. In the context of computing, you’d also talk about the backup copies that you have of your data. Outside of computing, you might come across a backup plan or a traffic backup. Police officers in trouble might radio in for backup.
To back up (two words), on the other hand, is an action. It is used as a verb. Again, the most common usage these days would be in the context of computing. You’re oftentimes reminded that you should back up all your data. If you’re in a parking lot, you might tell someone to back up into the parking spot. If you’re confused about something that someone said, you could ask them to back up and explain it to you again.
Realistically, most people aren’t going to fault you for using “backup” when you really mean to say “back up,” but you could fall into chipped mug syndrome. If you’re going to write anything, you may as well make the effort of being grammatically correct.
Do you have any suggestions for a future Grammar 101 topic? I’d love to hear them.