Since they did a subscription version which has channel in the discerption. The URL is even called channel4plus. Its all a little more complicated these days as more and more places are doing online channels.
Have you heard of Amazon channels? They are sort of a hybrid between TV channels and the OnDemand Apps. You turn on your Fire TV, scroll to channel pick what you like for example ITV or Discovery and subscribe. You then get a section called channels which lists ITV or which ever channel you subscribe to, there are over 150 channels depending on where you live. You then get access to that channel at higher quality then the free OnDemand App and no Adverts. For example the ITV channel is basically the ITVhub OnDemand app only better and enhanced, its a hybrid between the free APP and TV channel. Prices range around £2.99 and £4.99 a month depending on channel.
Thanks to Amazon confusing matters its not a case anymore that any channel is considered live TV.