Am I getting charged for using Wi-Fi?

Now, I'm using an Iphone 4, my recent bill stated that I had passed my data usage limit (1G) and I was charged extra for it.
I only use this at home where it is connected to my home Wi-Fi, which is on a different provider. I very rarely use it outside home to check my email etc. I have 3g on and cellular data off. So how did I pass my limit if I was using Wi-Fi?
Btw, how much megabytes does a 10 min video take?
And also what's the difference between 3G and cellular data?

Nope only if the persons Wi-Fi your using, does not have unlimted board band then they won't get charge extra for more usage.

Around 100 mb depending on the video quality

Doesn't charged from your card. A 10 min video can use almost 900 mb, it depends on format.
3g is a channel, cellular data is the packages that passes in the channel. In a pratical way, 3g is the speed that cellular data used to be presented.

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