Wifi hotspot and internet phones

If I understand using Smart phones  to connect to internet usually involves users purchasing a plan from internet provider, and as far as I know, most of them they are not unlimited (they have limited Gigs to use).
in the other side, there are Wifi Hotspots, these devices will allow users to connect their laptops to internet via Hotspot.
I believe Wifi Hotspot is like having wireless router at home, there is Unlimited usage of internet with flat rate. Correct?

I also want to know how the Internet provider assesses the usage of the smart phone usage when it is using internet ?  I mean if you do not download files through  your phone, will the internet size usage still be decremented , example if you have 2GB every month in your plan, browsing internet will decrement your 2GB ? how fast it will decrement it ?
I know that some people had to pay extra money , because their kids downloaded files from internet through their smart phones

Any clarification on this will be very appreciated.

Thanks