What is the difference between updating your iphone on iTunes or in your iphone?

So I'm trying to update my iPhone 4S and I don't have enough storage so I've heard that you can update it on iTunes. What I don't get is what difference does it make downloading it from iTunes or from your iphone directly

If you don't have space in your phone then you can't update, even through iTunes…

Updating straight off the phone: it needs to download the update to your iphone while your old iOS is still on the phone, and needs more room for it to extract and install the new iOS. So you will need extra memory to do this.

Updating with itunes: it downloads the update to your computer, extracts it then installs it to your phone, therefore it doesn't need as much memory as most of its done on the computer.

I probably didn't say everything right, but thats pretty much it.