Is this true if I use wireless lap top PC internet at home over certain...

Depends on who your ISP is and what terms you agreed to.

There are two types of wireless network.

802.11 aka WiFi. If you use this via a wireless router attached to your home broadband connection then there will be no charges that you wouldn't get if you used a wire.

3G - this uses mobile phone networks with billing done as per the contact you have for the 3G service

no, your wireless network is just to connect to your modem