Will using my phones wifi to connect to my wireless router cost when using the internet?

At the top bar of my phone it has -

Signal Bars
A 3G sign ( it changes from 3G to G to E, its really confusing i dont get it )
and then a wifi signal

When i tried going on the internet before i used the wifi the 3G/G ( bla bla bla you understand ) would go red and then arrows would go across it. When I connected to my wireless router the wifi signal would stay the same and an orange arrow would be used. The 3G thing would stay blue. It works really quick my internet and my apps, and i dont have internet in my contract - but this is wifi so isnt it different? Does it cost? Thanks xx
 
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